a stone is thrown horizontally from the top of a vertical wall with a velocity of 15m/s, hits the horizontal ground at a point 45m from the base of the wall. calculate the height of the wall. g=10m/s?
well, it takes 45/15 = 3 seconds to go 45m, so how far does a stone fall in 3 seconds?
h = 5 * 3^2 = 45 m
To find the height of the wall, we can use the equations of motion for a projectile.
Given:
Initial velocity (u) = 15 m/s (horizontal)
Distance traveled (horizontal range) = 45 m
Acceleration due to gravity (g) = 10 m/s^2
Let's break down the motion into horizontal and vertical components:
1. Horizontal motion:
The horizontal velocity (u) remains constant throughout the motion since there is no horizontal acceleration. Therefore, the time taken (t) to cover the horizontal distance of 45 m is given by:
Distance (s) = Velocity (v) × Time (t)
45 m = 15 m/s × t
t = 45 m / 15 m/s
t = 3 seconds
2. Vertical motion:
The stone is thrown horizontally, so the initial vertical velocity (v) is zero (since there is no initial upward or downward velocity).
Using the equation:
Distance (s) = Initial velocity (u) × Time (t) + 0.5 × Acceleration (a) × Time (t)^2
At the highest point, the vertical distance covered will be equal to the height (h) of the wall.
s = h
u = 0 m/s (since the stone has no initial vertical velocity)
t = 3 seconds
a = g = 10 m/s^2
Using the equation, we can find h:
h = u × t + 0.5 × a × t^2
= 0 m/s × 3 s + 0.5 × 10 m/s^2 × (3 s)^2
= 0 + 0.5 × 10 m/s^2 × 9 s^2
= 0 + 45 m
= 45 m
Therefore, the height of the wall is 45 meters.
To calculate the height of the wall, we can use the equations of motion. The stone is thrown horizontally, which means its initial vertical velocity is 0 m/s.
The horizontal distance traveled by the stone is 45 m, and its initial horizontal velocity is 15 m/s. We can use the formula for horizontal distance:
distance = velocity × time
Since the horizontal velocity is constant, we can rearrange the formula to solve for time:
time = distance / velocity
Substituting the given values:
time = 45 m / 15 m/s = 3 s
Now we need to find the height of the wall. We know that the stone is in free-fall vertically, so we can use the formula for vertical distance traveled:
distance = initial velocity × time + 0.5 × acceleration × time^2
Since the initial vertical velocity is 0 m/s, the formula simplifies to:
distance = 0.5 × acceleration × time^2
Substituting the given value of acceleration (g = 10 m/s²) and the previously calculated value of time, we can solve for distance:
distance = 0.5 × 10 m/s² × (3 s)^2 = 0.5 × 10 m/s² × 9 s² = 45 m
Therefore, the height of the wall is 45 meters.