A ball is thrown with a velocity of 20m/s. Find a]the maximum height t...
Projectile Motion Problem
Given:
- Initial velocity of the ball, u = 20m/s
- Acceleration due to gravity, g = 9.8m/s^2
Calculations:
Maximum Height:
The maximum height is obtained when the vertical component of the velocity is zero. Using the equation:
v^2 = u^2 + 2gh
where v = final velocity, u = initial velocity, g = acceleration due to gravity, and h = maximum height
At maximum height, v = 0
Therefore, 0 = 20^2 - 2(9.8)h
h = 20.4m
Time to reach Maximum Height:
The time taken to reach maximum height can be calculated using the equation:
h = ut + 0.5gt^2
where t = time taken
At maximum height, the final vertical velocity is zero.
Therefore, 0 = 20 - 9.8t
t = 2.04s
Time to return to the Thrower:
The total time of flight can be calculated using the equation:
t = 2u/g
where t = time of flight
Substituting the given values, we get:
t = 2(20)/9.8
t = 4.08s
Answer:
- The maximum height to which the ball rises is 20.4m.
- The time it takes to reach the maximum height is 2.04s.
- The time it takes to return back to the thrower is 4.08s.