A ball is thrown horizontally from a cliff at a speed of 15 m/s and strikes the ground 45 meters from the base of the cliff. How high was the cliff (rounded to the nearest meter)
it took the ball 45/15=3 seconds to travel 45 m horizontally
In those 3 seconds, it fell 4.9*3^2 = 44.1m, the height of the cliff
To determine the height of the cliff, we can use the equation of motion for an object in free fall. When the ball is thrown horizontally, the initial vertical velocity is zero (since there is no initial upward or downward motion) and the only force acting on the ball is gravity.
Using the equation for vertical displacement:
d = (1/2) * g * t^2
Where:
d = vertical displacement (height of the cliff)
g = acceleration due to gravity (approximated to 9.8 m/s^2)
t = time it takes for the ball to hit the ground
To find the time, we can use the horizontal velocity of the ball and the distance it travels:
v = d / t
Where:
v = horizontal velocity (15 m/s)
d = horizontal distance (45 m)
t = time
Solving for time, we get:
t = d / v
t = 45 m / 15 m/s
t = 3 s
Now, substituting the value of time into the equation for vertical displacement:
d = (1/2) * g * t^2
d = (1/2) * 9.8 m/s^2 * (3 s)^2
d = (1/2) * 9.8 m/s^2 * 9 s^2
d = 44.1 m
Therefore, the height of the cliff is approximately 44 meters (rounded to the nearest meter).
To find the height of the cliff, we need to determine how long it takes for the ball to hit the ground. We can use the formula:
distance = speed x time
In this case, we know the speed is 15 m/s, and the distance is 45 meters. Plugging these values into the formula, we can solve for time:
45 = 15 x time
Dividing both sides of the equation by 15 gives us:
time = 45 / 15
time = 3 seconds
Since the ball is thrown horizontally, it has no vertical velocity. The only force acting on the ball is gravity, causing it to accelerate downward at a rate of 9.8 m/s². Using the formula for vertical distance:
distance = initial velocity × time + (1/2) × acceleration × time²
We know the initial velocity is 0 m/s, the time is 3 seconds, and the acceleration is -9.8 m/s² (negative because it is downward). Plugging these values into the formula, we can solve for distance:
distance = 0 × 3 + (1/2) × (-9.8) × 3²
distance = (1/2) × (-9.8) × 9
distance = -44.1 meters
Since the distance is negative, it means the ball falls 44.1 meters below the base of the cliff. Adding this to the distance from the base of the cliff to the ground (45 meters), we can determine the height of the cliff:
height = 45 + 44.1
height = 89.1 meters
Therefore, the height of the cliff is approximately 89 meters.