Answer:
A. 29.7 m/s
B. 6.06 s
Explanation:
From the question given above, the following data were obtained:
Maximum height (h) = 45 m
A. Determination of the initial velocity (u)
Maximum height (h) = 45 m
Acceleration due to gravity (g) = 9.8 m/s²
Final velocity (v) = 0 m/s (at maximum height)
Initial velocity (u) =.?
v² = u² – 2gh (since the ball is going against gravity)
0² = u² – (2 × 9.8 × 45)
0 = u² – 882
Collect like terms
0 + 882 = u²
882 = u²
Take the square root of both side
u = √882
u = 29.7 m/s
Therefore, the ball must be thrown with a speed of 29.7 m/s.
B. Determination of the time spent by the ball in the air.
We'll begin by calculating the time take to reach the maximum height. This can be obtained as follow:
Maximum height (h) = 45 m
Acceleration due to gravity (g) = 9.8 m/s²
Time (t) to reach the maximum height =?
h = ½gt²
45 = ½ × 9. 8 × t²
45 = 4.9 × t²
Divide both side by 4.9
t² = 45/4.9
Take the square root of both side
t = √(45/4.9)
t = 3.03 s
Finally, we shall determine the time spent by the ball in the air. This can be obtained as follow:
Time (t) to reach the maximum height = 3.03 s
Time (T) spent by the ball in the air =?
T = 2t
T = 2 × 3.03
T = 6.06 s
Therefore, the ball spent 6.06 s in the air.
