question archive The figure (Intro 1 figure) shows the trajectory (i

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The figure (Intro 1 figure) shows the trajectory (i.e., the path) of a ball undergoing projectile motion over level ground. The time t_0 = 0\;\rm{s} corresponds to the moment just after the ball is launched from position x_0 = 0\;\rm{m} and y_0 = 0\;\rm{m}. Its launch velocity, also called the initial velocity, is v_vec_0.

Two other points along the trajectory are indicated in the figure.

* One is the moment the ball reaches the peak of its trajectory, at time t_1 with velocity v_1_vec. Its position at this moment is denoted by (x_1, y_1) or (x_1, y_{\max}) since it is at its maximum height.

* The other point, at time t_2 with velocity v_2_vec, corresponds to the moment just before the ball strikes the ground on the way back down. At this time its position is (x_2, y_2), also known as (x_{\max}, y_2) since it is at its maximum horizontal range.

Projectile motion is symmetric about the peak, provided the object lands at the same vertical height from which is was launched, as is the case here. Hence y_2 = y_0 = 0\;\rm{m}.

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What are the values of the intial velocity vector components v_0, x and v_0, y (both in m/s as well as the acceleration vector components a_0, x and a_0, y (both in m/s^2? Here the subscript 0 means "at time t_0."

The peak of the trajectory occurs at time t_1. This is the point where the ball reaches its maximum height y_max. At the peak the ball switches from moving up to moving down, even as it continues to travel horizontally at a constant rate.

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Q>

What are the values of the velocity vector components v_1, x and v_1, y (both in m/s as well as the acceleration vector components a_1, x and a_1, y (both in m/s^2? Here the subscript 1 means that these are all at time t_1.

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If a second ball were dropped from rest from height y_max, how long would it take to reach the ground? Ignore air resistance.

Check all that apply.

-t_0

-t_1

-t_2

-t_2 - t_1

-t_2/2

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Q*

Which of the following changes would increase the range of the ball shown in the original figure?

Check all that apply.

-Increase v_0 above 30 \rm{m/s}.

-Reduce v_0 below 30 \rm{m/s}.

-Reduce theta from 60 \rm{degrees} to 45 \rm{degrees}.

-Reduce theta from 60 \rm{degrees} to less than 30 \rm{degrees}.

-Increase theta from 60 \rm{degrees} up toward 90 \rm{degrees}.

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