Question

A well-thrown ball is caught in a well-padded mitt. If the acceleration of the ball is 2.10×10^4 m/s², and 1.85 ms elapses from the time the ball first touches the mitt until it stops, what is the initial velocity of the ball?

a) 38.85 m/s
b) 39.00 m/s
c) 39.15 m/s
d) 39.30 m/s

Answer 1

The initial velocity of the ball was found using the equation for uniformly accelerated motion (u = v - at), plugging in the deceleration value and the time. After computing, the initial velocity of the ball is determined to be 38.85 m/s.

Step-by-step explanation:

To find the initial velocity of the ball, we can use the equation for uniformly accelerated motion:

v = u + at

Where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Since the ball stops in the mitt, the final velocity v is 0 m/s. We rearrange the equation to solve for the initial velocity:

u = v - at

Plugging in the values:

• a (acceleration) = -2.10 × 104 m/s2 (negative because it's deceleration)

• t (time) = 1.85 ms = 1.85 × 10-3 s

• v (final velocity) = 0 m/s (since the ball stops)

Now we can calculate the initial velocity u:

u = 0 - (-2.10 × 104 m/s2) × (1.85 × 10-3 s)

u = 2.10 × 104 m/s2 × 1.85 × 10-3 s

u = 38.85 m/s

Therefore, the initial velocity of the ball was 38.85 m/s.