A grasshopper leaps into the air from the edge of a vertical cliff. Assume that

d1=7.15cm

, d2=1.04m

, and that

θ=49∘

A) what is the initial speed of the grasshopper?

B) what is the height of the cliff?

Maximum height reached h = 7.15cm = 0.0715 m The horizontal distance b = 1.04 m Angle of jump = 49 degrees. We have v^2 = 2gh which here is (vsin theta) ^2 = 2gh

v^2 = (2 x 9.81 x 0.0715) / sin^2 49 = 1.402 / - 0.95^2 = 1.55 = > v = 1.24 m/s

Time taken for flight = b / v Cos theta = 1.04 / (1.24 x cos49)

= 1.04 / 0.8135 = 1.27 s

Time to reach maximum height = vsin theta / g = (1.24 x 0.95) / 9.8 = 0.12 s

Now time taken for top to ground = 1.27 - 0.12 = 1.15 s

So the total height H = 1/2 gt = 1/2 x 9.8 x 1.15 = 5.635.

Now the height of the cliff = 5.635 - 0.0715 = 5.56 m