Chapter 10 MP (Extra Credit)

The crew of a cargo plane wishes to drop a crate of supplies on a target below. To hit the target, when should the crew drop the crate? Ignore air resistance.

Before the plane is directly over the target

When Dr. Hewitt releases the two projectiles, which one hits the ground first?

Both balls hit the ground at the same time.

In the previous part, you found that a pumpkin fired with an initial speed of 22 m/sm/s and an angle of 40∘40∘ reaches the same height as a pumpkin fired vertically with an initial speed of 14 m/sm/s. Which pumpkin takes longer to land?

Both pumpkins are in the air the same amount of time.

Why do the two objects hit the table at the relative times that they do?

Gravity pulls the same amount on each ball, and they each drop the same distance

What happens to the trajectory of the cannonball when you increase the diameter while keeping the mass constant?

Increasing the size makes the range of the trajectory decrease.

Predict how the vertical component of the velocity will change with time after the projectile is fired.

It first decreases to zero and then increases in the opposite direction.

Predict how the horizontal component of the velocity will change with time after the projectile is fired.

It stays constant.

Which ball (if either) has the greatest speed at the moment of impact?

The ball thrown horizontally

Consider the video demonstration that you just watched. A more complete explanation of what you saw will be possible after covering Newton's laws. For now, consider the following question: How would the result of this experiment change if we replaced the ball with another one that had half the mass? Ignore air resistance.

The ball would still land in the cart.

If the initial speed of the pumpkin is doubled, how does the maximum height change?

The maximum height increases by a factor of four.

Which projectile spends more time in the air, the one fired from 30∘∘ or the one fired from 60∘∘?

The one fired from 60∘

How does the range of the pumpkin change if its initial velocity is tripled (keeping the angle fixed and less than 90∘90∘)?

The pumpkin's range is nine times as far.

You might think that it is never a good approximation to ignore air resistance. However, often it is. Fire the cannonball without air resistance, and then fire it with air resistance (same angle and initial speed). Then, adjust the mass of the cannonball (increase it and decrease it) and see what happens to the trajectory. Don't change the diameter. When does the range with air resistance approach the range without air resistance?

The range with air resistance approaches the range without air resistance as the mass of the cannonball is increased.

So far in this tutorial, you have been launching a pumpkin. Let's see what happens to the trajectory if you launch something bigger and heavier, like a car. Compare the trajectory and range of the pumpkin to that of the car, using the same initial speed and angle (e.g., 45∘45∘). (Be sure that air resistance is still turned off.) Which statement is true?

The trajectories and thus the range of the car and the pumpkin are identical.

In the previous part, you discovered that the trajectory of an object does not depend on the object's size or mass. But if you have ever seen a parachutist or a feather falling, you know this isn't really true. That is because we have been neglecting air resistance, and we will now study its effects here. For the following parts, select the "Lab" mode of the simulation found at the bottom of the screen. Notice that you can adjust the mass and diameter of the object being launched. Turn on Air Resistance by checking the box. Fire a cannonball with an initial speed of 18 m/sm/s and an angle of 45∘45∘. Compare the trajectory to the case without air resistance. How do the trajectories differ?

The trajectory with air resistance has a shorter range.

Based on the figure, for which trajectory was the pumpkin in the air for the greatest amount of time?

Trajectory A

Consider the video you just watched. Suppose we replace the original launcher with one that fires the ball upward at twice the speed. We make no other changes. How far behind the cart will the ball land, compared to the distance in the original experiment?

four times as far