A few questions from my homework sheet that have me stumped. This is probably my weakest area in math. Thanks in advance and please show working out to the best you can. 
If I may have made a mistake typing the equations, values or whatever, just let me know.
1. A person standing on top of a 50m high cliff throws a pebble into the water with velocity 12ms^(-1) at an angle 30 degrees to the horizontal.
a. Using the base of the cliff as the origin, derive the equations for the horizontal and vertical components of the pebble's displacement (let g = 10ms^(-2) and neglect air resistance).
b. Calculate the time the pebble takes to land in the water and its distance from the base of the cliff.
2. A projectile is fired at an angle of 30 degrees above the horizontal with speed 20ms^(-1) from a stationary platform at ground level.
a. Find the horizontal range of the projectile.
b. By how much is the range increased if the platform is moving with speed 10ms^(-1) in the direction of the target? (g = 10ms^(-2))
3. Show that a particle is moving according to SHM if its displacement is given by: x = 3cos2t + 4sin2t, where x is in metres and t is in second. Find the maximum speed.
4. A particle is moving in SHM with acceleration: (d^2 x)/(dt^2) = -4xmms^(-2). If the particle starts at the origin with a velocity of 8mms^(-1), find the equation for its velocity in terms of its displacement.
If I may have made a mistake typing the equations, values or whatever, just let me know. 1. A person standing on top of a 50m high cliff throws a pebble into the water with velocity 12ms^(-1) at an angle 30 degrees to the horizontal.
a. Using the base of the cliff as the origin, derive the equations for the horizontal and vertical components of the pebble's displacement (let g = 10ms^(-2) and neglect air resistance).
b. Calculate the time the pebble takes to land in the water and its distance from the base of the cliff.
2. A projectile is fired at an angle of 30 degrees above the horizontal with speed 20ms^(-1) from a stationary platform at ground level.
a. Find the horizontal range of the projectile.
b. By how much is the range increased if the platform is moving with speed 10ms^(-1) in the direction of the target? (g = 10ms^(-2))
3. Show that a particle is moving according to SHM if its displacement is given by: x = 3cos2t + 4sin2t, where x is in metres and t is in second. Find the maximum speed.
4. A particle is moving in SHM with acceleration: (d^2 x)/(dt^2) = -4xmms^(-2). If the particle starts at the origin with a velocity of 8mms^(-1), find the equation for its velocity in terms of its displacement.
