Answer:
7 s
Explanation:
We'll begin by calculating the maximum height reached by the stone from the point of projection. This can be obtained as follow:
Initial velocity (u) = 29.4 m/s
Acceleration due to gravity (g) = 9.8 m/s²
Final velocity (v) = 0 m/s (at maximum height)
Maximum height (h) =?
v² = u² – 2gh (since the stone is going against gravity)
0² = 29.4² – (2 × 9.8 × h)
0 = 864.36 – 19.6h
Collect like terms
0 – 864.36 = –19.6h
–864.36 = –19.6h
Divide both side by –19.6
h = –864.36 / –19.6
h = 44.1 m
Next, we shall determine the time taken to reach the maximum height from the point of projection. This can be obtained as follow:
Initial velocity (u) = 29.4 m/s
Acceleration due to gravity (g) = 9.8 m/s²
Final velocity (v) = 0 m/s (at maximum height)
Time (t₁) take to reach the maximum height =?
v = u – gt (since the stone is going against gravity)
0 = 29.4 – (9.8 × t₁)
0 = 29.4 – 9.8t₁
Collect like terms
0 – 29.4 = – 9.8t₁
–29.4 = –9.8t₁
Divide both side by –9.8
t₁ = –29.4 / –9.8
t₁ = 3 s
Next, we shall determine the time taken for the stone to reach the ground from the maximum height reached by the stone. This can be obtained as follow:
Maximum height (H) from the ground = 34.3 + 44.1 = 78.4 m
Acceleration due to gravity (g) = 9.8 m/s²
Time (t₂) taken for the stone to reach the ground from the maximum height reached by the stone =?
H = ½gt₂²
78.4 = ½ × 9.8 × t₂²
78.4 = 4.9 × t₂²
Divide both side by 4.9
t₂² = 78.4 / 4.9
t₂² = 16
Take the square root of both side
t₂ = √16
t₂ = 4 s
Finally, we shall determine the total time taken for the stone to reach the ground. This can be obtained as follow:
Time (t₁) take to reach the maximum height = 3 s
Time (t₂) taken to reach the ground from the maximum height reached by the stone = 4s
Total time (T) taken to reach the ground =?
T = t₁ + t₂
T = 3 + 4
T = 7 s
Thus, it took the stone 7 s to reach the ground.
