Question

junior rides his trucycle off a level porch. If he left the porch at a speed of 4 m/s and landed a horizontal distance of 2.5m from the base, then what is the height of the porch?

Answer 1

the height of the porch is H=1.91 m

Explanation:

neglecting friction and assuming that the porch is horizontal, then the horizontal speed is v₀= 4 m/s and it does not change , thus he hits the base at

t= L/v₀ , L= horizontal distance

then for vertical motion , since the vertical velocity vy is 0 , the initial height is H ( the height of the porche) and the final height hf is 0 , we have

hf = H + vy*t - 1/2*g*t²

0 = H + 0 -1/2*g*t²

H = 1/2*g*t² = 1/2*g*(L/v₀)²

replacing values with g= gravity = 9.8 m/s²

H = 1/2*g*(L/v₀)² = 1/2*9.8 m/s² *( 2.5 m/ 4 m/s)² = 1.91 m

therefore the height of the porch is H=1.91 m