from the top of a tower which is 122.5 m high,a stone is thrown horizontally with a velocity of 5 m/s. what horizontal distance will be stone travel before hitting the ground
how long does it take to fall 122.5 meters?
4.9t^2 = 122.5
Use that value of t to figure how far it will travel at 5m/s.
To find the horizontal distance the stone will travel before hitting the ground, we need to understand the motion of the stone.
Given:
Initial velocity of the stone, u = 5 m/s (horizontal velocity)
Height of the tower, h = 122.5 m
We know that when a projectile is thrown horizontally, it only moves horizontally with a constant velocity. The vertical motion is affected by gravity.
The time taken for the stone to reach the ground can be found using the formula:
h = (1/2) * g * t^2
Where:
g is the acceleration due to gravity (approximately 9.8 m/s^2)
t is the time taken for the stone to reach the ground
Rearranging the formula to solve for t:
t = sqrt(2h/g)
Substituting the given values:
t = sqrt(2 * 122.5 / 9.8)
t ≈ sqrt(25)
t ≈ 5 s
Since the stone is thrown horizontally, the horizontal distance traveled can be calculated using the formula:
d = u * t
Substituting the given values:
d = 5 * 5
d = 25 m
Therefore, the stone will travel a horizontal distance of 25 meters before hitting the ground.
To determine the horizontal distance the stone will travel before hitting the ground, we need to calculate the time it takes for the stone to fall and then multiply that by the horizontal velocity.
First, let's calculate the time it takes for the stone to fall from the top of the tower to the ground using the formula for the time of flight (t) for an object in free fall:
t = sqrt((2 * h) / g)
where:
h = height of the tower = 122.5 m
g = acceleration due to gravity = 9.8 m/s^2
Plugging in the values, we get:
t = sqrt((2 * 122.5) / 9.8)
= sqrt(245 / 9.8)
= sqrt(25)
= 5 seconds
So, it takes 5 seconds for the stone to hit the ground.
Next, we multiply the time of flight by the horizontal velocity to find the horizontal distance traveled:
distance = velocity * time
= 5 m/s * 5 s
= 25 meters
Therefore, the stone will travel a horizontal distance of 25 meters before hitting the ground.