CIE A-levels Physics

On a planet, a vertically-launched projectile takes 12.5s to return to its starting position. The
projectile gains a maximum height of 170m. The planet does not have an atmosphere.
What is the acceleration of free fall on this planet?
A 2.2ms–2 B 8.7ms–2 C 27ms–2 D 54ms–2

Answer is B. Please explain & show me the working.

The first thing that I think of is energy. You should know that GPE=mgh where g is the acceleration due to gravity. So we need to find g. Next, we can look at the fact that this is actually free fall meaning that there are no resistive forces. This means that no work is done against air resistance so ALL of the kinetic energy is converted to gravitational potential energy. The equation for KE=0.5mv^2. We can equation these two equations to make 0.5mv^2=mgh. the m's will cancel, leaving us with 0.5v^2=gh. Then re-arrange for g and substitute your values. Hope this helps.

The first thing that I think of is energy. You should know that GPE=mgh where g is the acceleration due to gravity. So we need to find g. Next, we can look at the fact that this is actually free fall meaning that there are no resistive forces. This means that no work is done against air resistance so ALL of the kinetic energy is converted to gravitational potential energy. The equation for KE=0.5mv^2. We can equation these two equations to make 0.5mv^2=mgh. the m's will cancel, leaving us with 0.5v^2=gh. Then re-arrange for g and substitute your values. Hope this helps.

hi how to find the v?

On a planet, a vertically-launched projectile takes 12.5s to return to its starting position. The
projectile gains a maximum height of 170m. The planet does not have an atmosphere.
What is the acceleration of free fall on this planet?
A 2.2ms–2 B 8.7ms–2 C 27ms–2 D 54ms–2

Answer is B. Please explain & show me the working.