Question

A ball of mass 0.5 kg is thrown with kinetic energy of 100 J vertically upward. If air resistance is neglected, find maximum height reached by the ball. (g = 10 m/s²)

Answer 1

20 meters

Step-by-step explanation:

The initial velocity of the ball can be determined using the equation for kinetic energy:

K = (1/2)mv^2

100 J = (1/2) * 0.5 kg * v^2

So, v^2 = 200 J / 0.5 kg = 400 m^2/s^2

The velocity can be determined from the square root:

v = sqrt(400 m^2/s^2) = 20 m/s

Now we can use the velocity to determine the maximum height. The maximum height is reached when the velocity is zero, so we can use the formula for vertical motion under constant acceleration to find the time when this occurs:

v = v0 - gt

0 = 20 m/s - 10 m/s^2 * t

t = 2 s

We can use this time to find the maximum height:

h = v0 * t - (1/2)gt^2

h = 20 m/s * 2 s - (1/2) * 10 m/s^2 * 2 s^2

h = 40 m - 20 m

h = 20 m

So, the maximum height reached by the ball is 20 meters.