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A body is projected horizontally from the top of a tower with a velocity of 20m/s it landed on a grand level at a horizontal distance of 60m from the foot of the tower. Calculate the height of the tower (g=10m/s²)

Sagot :

Lucienashfordvillareidn

Answer:

To find the height of the tower, we can use the equations of motion for projectile motion under gravity. Here's how we can solve it:

To find the height of the tower:

Solution:

1. **Calculate the time of flight (\( t \))** using the horizontal distance (\( R \)):

- Given: Horizontal distance \( R = 60 \) m, Initial horizontal velocity \( u = 20 \) m/s

- Formula: \( t = \frac{R}{u} = \frac{60}{20} = 3 \) seconds

2. **Find the height (\( H \)) of the tower** using the vertical motion equation:

- Given: Acceleration due to gravity \( g = 10 \) m/s², Time of flight \( t = 3 \) seconds

- Formula: \( H = \frac{1}{2} g t^2 \)

- Substitute values: \( H = \frac{1}{2} \cdot 10 \cdot (3)^2 = \frac{1}{2} \cdot 10 \cdot 9 = 45 \) meters

Answer:

The height of the tower is 45 meters.

Explanation:

We first determine the time it takes for the projectile to travel horizontally using the given distance and initial velocity. Then, using this time, we calculate the height of the tower by considering the gravitational acceleration and the time squared, which gives us the vertical distance traveled.

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