When the object is thrown upwards or when the object is dropped from a height, the only force acting upon it is the gravitational force. Because of this, it simplifies equations of motion.
1. For the maximum height, the equation is
H = v₀²/2g
where
v₀ is the initial speed
g is the acceleration due to gravity equal to 9.81 m/s²
For the blue ball, v₀ = 21.6 m/s. Substituting the values:
H = (21.6 m/s)²/2(9.81m/s²)
H = 23.78 m
The maximum height reached by the blue ball is 23.78 m + 0.8 = 24.58 m.
2. The distance traveled with any given distance is calculated using the formula:
y = v₀t + 0.5gt²
where y is the distance at any time t
For the red ball, v₀ = 8.3 m/s. Substituting the values:
y = (8.3 m/s)(3.38 s) + 0.5(9.81 m/s²)(3.38 s)²
y = 84.09 m
The red ball would reach 84.09 m after 3.38 seconds.
3. For this, you equate the y values of both balls:
y for red ball = y for blue ball
v₀t + 0.5gt² = v₀t + 0.5gt²
(8.3 m/s)t + 0.5(9.81 m/s²)(t²) + 26.1 m = (21.6 m/s)t + 0.5(9.81 m/s²)(t²) + 0.8 m
Solving for t,
t = 1.9 seconds
Thus, the two balls would be at the same height after 1.9 seconds.
