Question

At time t = 0, a student throws a set of keys vertically upward to her sorority sister, who is in a window at distance h above. The second student catches the keys at time t. (a) With what initial velocity were the keys thrown? (b) What was the velocity of the keys just before they were caught?

Answer 1

To determine the initial velocity, we can find the time taken for the keys to reach the sorority sister using the equation for vertical motion. The velocity just before the keys were caught is equal to the initial velocity.

Step-by-step explanation:

To determine the initial velocity with which the keys were thrown, we need to find the time it took for the keys to reach the sorority sister. By solving for time using the equation for vertical motion, we find that it took approximately 3.96 seconds. Next, we can use the initial vertical velocity and the time to find the initial velocity using the equation:

v = u + at

The velocity of the keys just before they were caught can be found by subtracting the vertical component of the final velocity from the initial velocity. Since the keys were caught at the same height from which they were thrown, the vertical component of the final velocity is zero. Therefore, the velocity just before they were caught is equal to the initial velocity.

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