Question

A ski jumper competing for an Olympic gold medal wants to jump a horizontal distance of 135 meters. The

takeoff point of the ski jump is at a height of 25 meters. With what horizontal speed must he leave the jump?
a. What do you know?
b. What do you need to solve for?
c. What equation(s) will you use?
d. What is the solution to this problem?

Answer 1

The ski jumper must leave the jump with a horizontal speed of 31 m/s.

Step-by-step explanation:

To calculate the horizontal speed at which the ski jumper must leave the jump, we can use the principle of conservation of mechanical energy. At the takeoff point, the ski jumper has potential energy due to the height and no kinetic energy. At the landing point, the ski jumper has no potential energy and only horizontal kinetic energy.

Since potential energy is given by PE = mgh and kinetic energy is given by KE = 1/2mv^2, we can equate the initial potential energy to the final kinetic energy to obtain:

mgh = 1/2mv^2

where m is the mass, g is the acceleration due to gravity, h is the height, and v is the horizontal speed.

Cancelling the mass terms and rearranging the equation, we get:

v = sqrt(2gh)

Substituting the values of g = 9.8 m/s^2 and h = 25 m, we can solve for v:

v = sqrt(2 * 9.8 * 25) = 31 m/s

Answer 2

a) I know that the take off height is 25m. I also know that the horizontal distance to cover is 135m.

b) I need to solve the take off horizontal speed from the height.

c) The equation is Horizontal distance, x = Horizontal speed u * time t.
x = ut

H = (1/2)gt^2. Taking g as 10 m/s^2

Where H = Take off height from the ground.

Using second equation:

H = (1/2)gt^2

25 = (1/2)*10* t^2

25 = 5t^2

5t^2 = 25

t^2 = 5. Therefore, t = √5 seconds.

Using x = ut

125 = u * √5

u = 125/√5. Expressing as surd u = 25√5 m/s.

Using your calculator, u = 55.90 m/s.