A clump of soft clay is thrown horizontally from 78.40 m above the ground with a speed of 27.0 m/s. Where is the clay after 4.5 s? Assume it sticks in place when it hits the ground.
horizontal ....m from the launch position
vertical ....m from the ground
With no initial vertical velocity component, it hits the ground after time T given by
78.4 = (g/2) T^2
T = 4.00 s
It's horizontal location is the initial (horizontal) velocity muliplied by that time. It does not move after that.
To determine where the clay is after 4.5 seconds, we need to find the horizontal and vertical distances it covers during that time.
First, let's calculate the horizontal distance. Since the clay is thrown horizontally, its horizontal speed will remain constant throughout its flight. We can use the formula:
horizontal distance = horizontal speed × time
Given that the horizontal speed is 27.0 m/s and the time is 4.5 seconds, we have:
horizontal distance = 27.0 m/s × 4.5 s = 121.5 m
So, the clay will be 121.5 meters horizontally from the launch position after 4.5 seconds.
Next, let's calculate the vertical distance. Since the clay is affected by gravity, its vertical displacement will depend on its initial vertical speed, the time, and the gravitational acceleration. We can use the formula:
vertical distance = (initial vertical speed × time) + (0.5 × gravitational acceleration × time²)
The initial vertical speed is zero because the clay is thrown horizontally, and the gravitational acceleration is approximately 9.8 m/s².
vertical distance = (0 × 4.5 s) + (0.5 × 9.8 m/s² × (4.5 s)²)
vertical distance = 0 + (0.5 × 9.8 m/s² × 20.25 s²)
vertical distance = 99.45 m
So, the clay will be 99.45 meters above the ground after 4.5 seconds.
To determine the final position of the clay, we need to combine the horizontal and vertical distances:
Final position = (horizontal distance from launch position, vertical distance from the ground)
Final position = (121.5 m horizontally, 99.45 m above the ground)
Therefore, after 4.5 seconds, the clay will be located 121.5 meters horizontally from the launch position and 99.45 meters above the ground.