A stone is thrown vertically downwards from a building with an initial speed of 4m/s.It reached the ground after 5 s. (a) whats the height of the building h?
using g=10m/s^2, we have
h - 4t - 5t^2 = 0
h - 20 - 125 = 0
h = 125 m
h = 145 m ?.
132.5
To find the height of the building, we can use the equation of motion for vertical downward motion:
h = h0 + v0t + (1/2)gt^2
Where:
- h is the height of the building
- h0 is the initial height (which is the building height)
- v0 is the initial velocity of the stone (4 m/s)
- t is the time taken for the stone to reach the ground (5 s)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
In this case, since the stone was initially thrown downwards, the initial velocity is negative. Therefore, we can replace v0 with -4 m/s in the equation.
Plugging in the given values, we get:
h = h0 + (-4) * 5 + (1/2) * 9.8 * 5^2
Simplifying further:
h = h0 - 20 + 122.5
h = h0 + 102.5
Since the stone reaches the ground, its final height is 0. Therefore, h0 = -102.5.
Therefore, the height of the building, h, is 102.5 meters.