Physics, 27.02.2021 14:00 bethanymorris155

a stone is thrown vertically upward with a velocity of 29.4m/s from the top of tower 34.3m high. calculate the total time taken by the stone to reach the foot of the tower.

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Answer from: edtorres5

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.

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