Final answer:
To find the initial speed at which Tom kicked the rock, we can use the formulas for the horizontal and vertical motion of a projectile.
Step-by-step explanation:
To find the initial speed at which Tom kicked the rock, we can use the formula for the horizontal motion of a projectile:
d = v0x * t
Where d is the horizontal distance (45.0 m), v0x is the initial horizontal velocity (which is the speed at which the rock was kicked), and t is the time of flight.
Since the rock was kicked horizontally, the initial vertical velocity is 0 m/s, and the vertical motion can be described by the formula:
d = v0y * t + (1/2)*g*t2
Where v0y is the initial vertical velocity, which is 0 m/s, g is the acceleration due to gravity (9.8 m/s2), and t is the time of flight.
Since the rock starts at a height of 20.0 m and hits the ground, the vertical displacement can be calculated as:
20.0 m = (1/2)*g*t2
By solving this equation for t, we can find the time of flight, which will allow us to find the initial horizontal velocity v0x.
Substituting the value of t into the equation for horizontal motion, we can solve for v0x