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
In those 3 seconds, it fell 4.9*3^2 = 44.1m, the height of the cliff
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).
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.