please help with this question?

Question

a skier launches off a hill with a horizontal speed Vo. the hill below slopes away at an angle theta.
a) derive an equation for d, the distance down the hill whee the skier lands in terms of Vo and theta.
b)if the skier on the next jump increases Vo by 5%, by what percentage does the distance traveled increase?

Answer 1

If d is the distance along the slope,

d sin ө = ½ g t^2. (d sin ө’ is the vertical height)

d cos ө = Vo*t ( d cos ө is the horizontal distance)

Eliminating‘t’ from the first using the second equation,

d = 2 Vo^2 tan ө * sec ө

Since d is proportional to Vo^2,

d2/d1 = (0.05)^2 = 0.0025 = 0.25 %

Answer 2

The equation of motion that binds velocity, distance travelled and acceleration together is: v^2 = u^2 + 2*g*h
Where u = initial vel., v= end vel., g = acceleration, h = dist travelled.
Using your data, we have u = Vo*cos(theta), g = g *sin(theta),
h = d;
Substitute in above eqn
v^2 = Vo^2 *cos^2(theta) + 2 * g *sin(theta) * d

Answer 3

use the common sense dumbo