Question

A well-thrown ball is caught in a well-padded mitt. If the deceleration of the ball is 2.10×10^4 m/s², and 1.85 ms (1 ms=10^(-3) s) elapses from the time the ball first touches the mitt until it stops, what was the initial velocity of the ball?

a) -39.0 m/s
b) -37.5 m/s
c) 39.0 m/s
d) 37.5 m/s

Answer 1

Using the kinematic equation to calculate for the initial velocity with the given deceleration of 2.10 x 10^4 m/s² and time of 1.85 x 10^-3 s, the initial velocity of the ball is found to be 39.0 m/s.

Step-by-step explanation:

To find the initial velocity of the well-thrown ball that is caught in the mitt, we use the kinematic equation which relates velocity, acceleration, and time:
v = u + at, where v is the final velocity (0 m/s since the ball stops), u is the initial velocity (what we're looking for), a is the deceleration, and t is the time.

Rearranging the equation to solve for u, we get: u = v - at. Since we're given the deceleration a = -2.10 × 10´ m/s² (negative because it's a deceleration) and the time t = 1.85 ms, which is actually 1.85 × 10⁻³ seconds, we can plug these values into our rearranged equation.

Substituting the given values: u = 0 m/s - (-2.10 × 10´ m/s²) × (1.85 × 10⁻³ s), we then calculate u.

u = 39.0 m/s

So, the initial velocity of the ball was 39.0 m/s.