Question

A ball is shot straight up in the air from the surface of the earth with an initial speed of 19.6 m/s. What max height will the ball reach?

A) 9.80 m
B) 14.7 m
C) 19.6 m
D) 24.5 m
E) 58.8 m

Answer 1

Using kinematic equations and the initial velocity of 19.6 m/s, the maximum height a ball will reach when shot straight up is 19.6 meters.

Step-by-step explanation:

The question involves calculating the maximum height a ball will reach when shot straight up with an initial speed of 19.6 m/s, assuming no air resistance and using Earth's gravitational acceleration. To find the maximum height, we can use the following kinematic equation that relates initial velocity, acceleration due to gravity, and displacement:

vf2 = vi2 + 2ad

Where vf is the final velocity (0 m/s at the maximum height), vi is the initial velocity (19.6 m/s), a is the acceleration due to gravity (-9.8 m/s2, negative because it is in the opposite direction to the velocity), and d is the displacement, which in this case, will be the maximum height reached.

We solve for d like so:

0 = (19.6 m/s)2 + 2(-9.8 m/s2)d

d = (19.6 m/s)2 / (2 × 9.8 m/s2)

d = 19.6

Therefore, the maximum height the ball will reach is 19.6 meters, which corresponds to option C.