A block starts at rest and slides down a fric-

tionless track.
The acceleration of gravity is 9.81 m/s2 .
It leaves the track horizontally, striking the
ground (as shown in the figure above).
b b b
b
b
b
b
b
b
b
b
b
502 g
h
2.2 m
4.4 m
9.81 m/s2
a) At what height h above the ground is the
block released?
Answer in units of m

To determine the height h above the ground at which the block is released, we can use the principles of conservation of energy.

Step 1: Write down the conservation of energy equation in terms of potential energy and kinetic energy:

Potential Energy at height h + Kinetic Energy at height h = Potential Energy at ground level + Kinetic Energy at ground level

Step 2: Recognize that at height h, the block is at rest, so its kinetic energy is zero.

Potential Energy at height h = Potential Energy at ground level + Kinetic Energy at ground level

Step 3: Substitute the formulas for potential energy and kinetic energy into the equation:

mgh = 0 + (1/2)mv^2

where m is the mass of the block (given as 502g, which is 0.502kg), g is the acceleration due to gravity (given as 9.81m/s^2), and v is the velocity of the block at ground level (which we assume to be the same as its velocity when it leaves the track).

Step 4: Solve for height h:

h = (1/2)v^2/g

Step 5: Determine the velocity v at ground level. Since the block leaves the track horizontally, it will continue to move horizontally until it reaches the ground. Therefore, its horizontal speed will remain constant.

Step 6: Calculate the velocity v using the horizontal distance traveled by the block. From the figure, the horizontal distance is given as 4.4m.

v = d/t

where d is the horizontal distance and t is the time it takes for the block to travel that distance. Since the block starts at rest, we can use the formula for constant acceleration to calculate the time:

d = (1/2)at^2

Solve for t:

t = sqrt(2d/a)

Substitute the values for d and a:

t = sqrt(2 * 4.4m / 9.81m/s^2)

Step 7: Substitute the calculated velocity v and acceleration due to gravity g into the equation for height h:

h = (1/2) * (sqrt(2 * 4.4m / 9.81m/s^2) )^2 / 9.81m/s^2

Simplify and calculate the value for h to get the answer in units of meters.