Question

a bmx bicycle rider takes off from a ramp at a point 2.4 m above the ground. the ramp is angled at 40∘ from the horizontal, and the rider's speed is 7.5 m/s when he leaves the ramp.

Answer 1

To find the initial speed of the mountain biker, we can use the concept of projectile motion. By using the formulas for vertical and horizontal displacement, we can solve for the initial speed.

Step-by-step explanation:

To find the initial speed of the mountain biker, we can use the concept of projectile motion. Since the biker lands 20 m below their launch point, we can determine the vertical displacement using the formula:

d = V_i * t + (1/2) * a * t^2

where d is the vertical displacement, V_i is the initial vertical velocity, t is the time of flight, and a is the acceleration due to gravity (-9.8 m/s²). Substituting the known values, we have:

20 m = V_i * t + (1/2) * (-9.8 m/s²) * t^2

Next, we can use the fact that the biker lands at a horizontal distance of 45.0 m to determine the horizontal displacement. The horizontal displacement is given by:

d = V_i * t

Substituting the known values, we have:

45.0 m = V_i * t

We can now solve these two equations simultaneously to find the initial speed of the mountain biker.