A ball is projected horizontally from the top of a hill with a velocity of 30m/s.If it reaches the ground 5 seconds later,calculate the height of the hill,take g=10 metres per second square.
The horizontal speed does not matter.
In time t the ball falls 5t^2 meters
so, ...
To find the height of the hill, we can use the formula for vertical motion:
h = (1/2)gt^2
where h is the height, g is the acceleration due to gravity (10 m/s^2), and t is the time taken (5 seconds).
Since the ball is projected horizontally, there is no initial vertical velocity. Therefore, the initial height is zero.
Plugging the values into the formula, we get:
h = (1/2)(10)(5)^2
h = (1/2)(10)(25)
h = 125 meters
Therefore, the height of the hill is 125 meters.
To calculate the height of the hill, we first need to find the time it takes for the ball to reach the ground horizontally.
Since the ball is projected horizontally, the initial vertical velocity is 0 m/s. The only force acting on the ball vertically is gravity, which accelerates it downwards at a rate of -10 m/s^2.
We know that the time taken for an object to reach the ground from rest, with an initial velocity of 0 m/s and an acceleration of -10 m/s^2, is given by the formula:
t = sqrt(2h/g)
Where:
t = time taken
h = height
g = acceleration due to gravity
Rearranging the formula to solve for height, we get:
h = (g * t^2) / 2
Now we can substitute the given values into the equation:
h = (10 m/s^2 * (5 s)^2) / 2
h = (10 m/s^2 * 25 s^2) / 2
h = (250 m^2/s^2) / 2
h = 125 m
Therefore, the height of the hill is 125 meters.