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?

the height of the porch is H=1.91 m

Step-by-step 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