# Vertical Motion Problems

1. Football Problem

A football is kicked into the air with an initial upward velocity of 25 meters per second. (m/sec)

Calculate it’s height after 2 seconds.

Calculate it’s height after 3 seconds.

When will it be 20 meters above the ground?

When will the ball hit the ground?

1. Baton Problem

A twirler throws a baton with an initial upward velocity of 20 meters per second (m/sec).

Calculate it’s height after 2 seconds.

When will it be 15 meters above where it was thrown?

When will the baton be back at the twirler’s level?

1. Pop Fly Problem

Milt Famey, the baseball player, hits a pop fly to the infield. It goes upward with an initial velocity of 30 (m/sec).

What is the altitude after 2 seconds?

When is it 25 meters above where it was hit?

When is it back down?

The ball is at it’s highest halfway between the time it was hit (t=0) and the time it gets back down. (see part c)

When is it at it’s highest?

The ball will be at his highest at 3 seconds. (1/2 of 6)

What is it’s highest distance?

1. Cannonball Problem

A cannonball is fired with an initial upward velocity of 100m/s.

Calculate it’s altitude after 3 seconds.

At what times will it be 480 meters high?

The cannonball reaches it’s highest point halfway between the time it is fired (t=0)and the time it hits the ground.

When will it reach it’s highest?

How high is it at it’s highest?

1. Snoopy’s Dogfight Problem

Snoopy is flying in his Sopwith Camel. He fires at the Red Barron.  The bullet has an upward initial velocity of 120m/sec.

The Red Barron is 400 meters above Snoopy. When will the bullet first reach his altitude?

The bullet misses on the way up. Could it hit the Red Barron on it’s way back down?

If the bullet also misses the Red Barron on it’s way down, will it be back at the level with Snoopy’s Sopwith Camel?

If it misses Snoopy on the way down, when will it hit the ground, 900 meters below where it was fired?

1. Rock off the Cliff Problem

Suppose that you throw a rock into the air from the top of a cliff. The initial upward velocity is 15 (m/sec).

How high will the rock be above the cliff top after 2 seconds?

Where will it be after 4 seconds?

When will it again be at the same level you threw it?

When will it hit the water, 50 meters below where you threw it?

1. Clown’s Cannon Problem

At the circus, Art Tillery is fired into the air from a cannon on a platform. His initial upward velocity is 7m/sec.

How high is he above the firing point after 0.6 seconds?

When will be 2 meters above his firing point?

When will he be back at the level of the cannon?

When will he land in the tank of water, 20 meters below his firing point?

Wile E. Coyote is standing on a springboard atop the high cliff. Roadrunner drops a boulder on the other end of the springboard, sending Wile up with an initial velocity of 45m/sec.

How high will Wile be after 4 seconds?

At what other time will he be the same altitude as above?

At 4 seconds, was Wile going up or down?

Going up since he was at 100 meters later, at 5 seconds, going down.

When does he reach the level of the springboard?

On the way down, Wile misses the cliff. At what time does he land in the river 120 meters below the top of the cliff?

1. Chuck’s Rock Problem

Chuck throws a rock with an initial upward velocity of 12m/sec.

How high is it after 0.7 seconds?

When will it be 7.2 meters up?

At the time in the problem above, is it going up or down?

It was neither going up nor down. It had reached its high point since there was only one value of t.

When does the rock get back to the ground level?

On the way down, the rock goes straight down a well, splashing at the bottom 4 seconds after it was thrown. How deep is the well?

1. Ski Jump Problem

As Al Pine jumps off the end of a ski jump, he has an initial velocity of 13 meters/second.

How high will he be 2 seconds after he jumps?

At what other time will he be as in the problem above?

At 2 seconds, was Al going up or down?

Going down since he was at 6 meters earlier, at 0.6 seconds, going up.

When is he at the level of the ski jump again?

Al spends a total of 5.2 seconds in the air. How far below the end of the ski jump does he land?

A basketball player shoots a long shot. The ball has an initial upwards velocity of 6 meters/seconds. When it is released, it is at the same level of the basket.

After 0.3 seconds, how high is the ball above the basket?

The basket is three meters above the gym floor. After 0.3 seconds, how high is the ball above the gym floor?

Assuming the aim is good, when will the ball go into the basket?

The ball is highest halfway between the time it is thrown and the time it goes into the basket.

-What time is this?

-How high is the ball above the gym floor?

1. Volleyball Problem

In an underhand volleyball serve, the ball leaves the server’s hand 1 m above the floor. Suppose that it’s initial upward velocity is 7m/sec.

How high above the floor will it be after 0.3 seconds?

If nobody else touches it, when will it be back to the level where it was served?

If nobody else touches it, when will it be down on the floor?

The ball reaches the highest level halfway between the time it is served and the time it is back at the same level.

-What time is this?

-How high above the floor then?

1. Golf Problem

A golf ball is hit high into the air with an initial up-ward velocity of 33 m/sec.

How high is it after 3 seconds?

When will it be 29 meters above the ground?

Substitute 60 for d and try to solve for t.  What does this tell you about when the ball will be 60 m up?

1. Naval Gunnery Problem

Big guns on naval ships must fire projectiles many kilometers. To do this, the projectile must go high into the air. Suppose that the initial upward velocity of a projectile is 300 m/sec.

How high will the projectile be 20 seconds after it is fired?

When will it reach 1 kilometer above where it was fired?

Will it ever be 5,000 meters above where it was fired?

How long does it take to reach the target, which is at the same level as the projectile was fired?

1. Moon Jumping ProblemAn astronaut on the earth practices jumping to the ground from a spaceship resting three meters above the ground. The initial upward velocity of the jump is 4 m/sec.

When will the astronaut be back at the same level as the jump?

At what time is the highest point reached?

How high above the ground is that?

When does the astronaut reach the ground?

When the astronaut is on the moon, the gravity is much weaker.

The equation there is:

Suppose the initial velocity of the jump is still 4 m/sec.

When will the astronaut be at the same level as the jump?

How high above the moon’s surface does the astronaut go?

When does the astronaut land on the moon’s surface?

1. Sports on the Moon Problem

Since gravity is much weaker on the moon, an

object thrown upward from its surface reaches an altitude d given by

Find the time it takes for each of the following to return to the level from which they started.

A high jumper, r = 7 m/seconds.

A baseball, r = 30 m/seconds.

A golf ball, r = 33 m/seconds.

An arrow, r = 50 m/seconds.

Each of the above will be at its maximum altitude halfway between the time it starts and the time it gets back down. Find the maximum altitude for each object above.

A high jumper, r = 7 m/seconds.

A baseball, r = 30 m/seconds.

A golf ball, r = 33 m/sec.

An arrow, r = 50 m/seconds.

1. Rhoda’s Motorcycle Problem

Rhoda Davidson prepares to jump her motorcycle from one 2 foot ramp to another.  Since precise calculations are essential to her safe landing, she uses the equation

in which 5 is replaced by the more precise value 4.893, which is the value at her latitude, 20 degrees.

If she takes off with an upward initial velocity  of r = 13.7 m/sec.

When will she land on the down ramp?

What is the highest she goes above the ground?

If her time of flight is to be precisely 3.7 seconds?

What must her initial upward velocity be?

What is the highest she goes above the ground?

If her initial upward velocity is r = 11 m/sec, will she ever be 9 meters above the ground (7 meters above the top of the ramp) ?   Justify your answer.

1. Diving Board Problem

Suppose that you spring into the air from the 3-meter diving board. You hit the water, 3 meters below the board, at 1.6 seconds from the time you sprang.

What was your initial upward velocity, r ?

When do you pass the board on your board on your way back down?

How high above the board did you go?

If you spring from the 1-meter board with the same initial upward velocity as in the first question above, when will you hit the water?

If another diver steps off the 10 meter platform (initial velocity is r = 0) at the same time as you spring from the 3-meter board who reaches the water sooner? How much sooner?

That’s all folks.