A sled is initially given a shove up a frictionless 32.0 incline. It reaches a maximum vertical height 1.50 higher than where it started.
Imcomplete.
To find the speed at which the sled was initially given a shove, we can use conservation of energy.
The initial kinetic energy (KE) of the sled is converted into potential energy (PE) at the highest point of its trajectory.
The formula for gravitational potential energy is given by PE = mgh, where m is the mass of the sled, g is the acceleration due to gravity, and h is the height.
Let's assume the mass of the sled is m, the acceleration due to gravity is 9.8 m/s², and the height is 1.50 m.
Using conservation of energy, the initial kinetic energy is equal to the final potential energy:
(1/2)mv² = mgh
Since the mass cancels out, we can solve for the initial velocity (v):
(1/2)v² = gh
v² = 2gh
v = √(2gh)
Plugging in the values, we get:
v = √(2 * 9.8 * 1.50)
v ≈ √29.4
v ≈ 5.42 m/s
Therefore, the sled was initially given a shove with a speed of approximately 5.42 m/s.