Question

How fast does a truck have to travel to jump 85 yards in the air with the ramp being 6 ft. tall and a angle of 14 degrees

Answer 1

consider the motion in vertical direction :

Y_f= final maximum height gained = 85 yards = 85 x 0.9144 m = 77.72 m (Since 1 yard = 0.9144 m)

Y_i= initial position at the top of ramp = height of ramp = 6 ft = 6 x 0.3048 m = 1.83 m (Since 1 ft = 0.3048 m)

v = initial velocity of launch

= angle of launch = 14 deg

v_oy = initial velocity in Y-direction = v Sin = v SIn14

v_fy = final velocity at the maximum height = 0 m/s

a = acceleration = acceleration due to gravity = - 9.8 m/s²

using the equation

v_fy² = v_oy² + 2 a (Y_f - Y_i)

inserting the values

(0)² = (v Sin14)² + 2 (- 9.8) (77.72 - 1.83)

v = 159.42 m