A grasshopper leaps into the air from the edge of a vertical cliff, as shown in the figure below. a.) Use information from the figure to find the initial speed, in m/s, of the grasshopper. b.) Use information from the information below to find the height, in m, of the cliff.
The grasshopper jumps at an angle of 50, reaching a maximum height of 6.74 cm above the cliff, and hitting the ground below the cliff 1.06 m away.
2 Answers

Let v be the magnitude of velocity of grasshopper
(v sin50)^2 = 2×9.8×0.0674 or v^2 = 1.32104/ sin^2 50 = 2.2512 or
v =1.5 m/s
Time of flight 1.06/ (v cos 50) = (1.06/1.5)/cos 50 = 1.099s
Time to reach maximum height = (1.5 sin 50)/9.8 =0.1175 s
The time taken for grasshopper to come down from the topmost position = 0.9815 s
The total height travelled from topmost position
0.5×9.8×0.9815 = 4.809
Height of cliff = 4.8093 – 0.0674 = 4.742 m

The people who answer this stuff are idiots for not giving the original formula or where they got numbers from.