Answer:
3.3 s
Step-by-step explanation:
From the question given above, the following data were obtained:
Initial velocity (u) = 12 m/s
Height of tower (h₁) = 15 m
Total time (T) to reach the ground =?
Next, we shall determine the time taken to reach the maximum height from the tower. This can be obtained as follow:
Initial velocity (u) = 12 m/s
Final velocity (v) = 0 m/s (at maximum height)
Acceleration due to gravity (g) = 10 m/s²
Time (t₁) to reach the maximum height from tower =?
v = u – gt₁ (ball is going against gravity)
0 = 12 – 10t₁
Rearrange
10t₁ = 12
Divide both side by 10
t₁ = 12/ 10
t₁ = 1.2 s
Next, we shall determine the maximum height reached by the ball from the tower.
Initial velocity (u) = 12 m/s
Final velocity (v) = 0 m/s (at maximum height)
Acceleration due to gravity (g) = 10 m/s²
Maximum height from the tower (h₂) =?
v² = u² – 2gh₂
0² = 12² – 2 × 10 × h₂
0 = 144 – 20h₂
Rearrange
20h₂ = 144
Divide both side by 20
h₂ = 144 / 20
h₂ = 7.2 m
Next, we shall determine the maximum height from the ground. This can be obtained as follow:
Height of tower (h₁) = 15 m
Maximum height from the tower (h₂) = 7.2 m
Maximum height from the ground (H) =?
H = h₁ + h₂
H = 15 + 7.2
H = 22.2 m
Next, we shall determine the time taken for ball to get to the ground from the maximum height. This can be obtained as follow:
Acceleration due to gravity (g) = 10 m/s²
Maximum height from the ground (H) = 22.2 m
Time (t₂) taken for ball to get to the ground from the maximum height =?
H = ½gt₂²
22.2 = ½ × 10 × t₂²
22.2 = 5 × t₂²
Divide both side by 5
t₂² = 22.2 / 5
t₂² = 4.44
Take the square root of both side
t₂ = √4.44
t₂ = 2.1 s
Finally, we shall determine the time taken for the ball to get to the ground. This can be obtained as follow:
Time (t₁) to reach the maximum height from tower = 1.2 s
Time (t₂) taken for ball to get to the ground from the maximum height = 2.1 s
Time (T) taken for the ball to get to the ground =?
T = t₁ + t₂
T = 1.2 + 2.1
T = 3.3 s
Therefore, it will take the ball 3.3 s to get to the ground.