A child slides up a playground ramp with a speed of 4 m/s. How high up the ramp will the child go? (Assume no friction.)

The initial speed (velocity) of the child is $v = 4 \text{ m/s}$.
We need to find the maximum height $h$.
The acceleration due to gravity is $g = 9.8 \text{ m/s}^2$.
When the child slides up the ramp, their initial kinetic energy is converted into gravitational potential energy at the maximum height. We use the principle of conservation of mechanical energy:

The mass $m$ of the child cancels out from both sides.

The child will go $\boxed{\text{0.82 m}}$ high up the ramp.

Question 8:

a) A truck of mass $2000 \text{ kg}$ moves up a hill at $20 \text{ m/s}$. Find the maximum height reached. Then state whether mass affects the height.

The mass of the truck is $m = 2000 \text{ kg}$.
The initial speed (velocity) of the truck is $v = 20 \text{ m/s}$.
We need to find the maximum height $h$.
The acceleration due to gravity is $g = 9.8 \text{ m/s}^2$.
Using the principle of conservation of mechanical energy:

Again, the mass $m$ cancels out from both sides.

The maximum height reached by the truck is $\boxed{\text{20.41 m}}$.

As seen in the formula $h = \frac{v^2}{2g}$, the mass $m$ is not present. This means that for a given initial velocity, the maximum height reached is independent of the mass of the object.
No, the mass does not affect the height reached.