Mathematics and geometry

Question

A stone is released from rest at the top of Clif 194.8m high. At the same time a lorry move from rest towards the Clif. If the distance between the Clif and and lorry is 75m, Calculate the speed at which the lorry should run for the stone to fall inside the lorry.

Take g = 10m/s²

U can also use any approved constant in mathematics and physics. Ur time start now...

Answer 1

Find t_air from d = 1/2 gt² solved for d = height and t = t_air

t_{air = sqrt(2h/g)= sqrt(2* 194.8 m /10 m/s}²) =6.242 seconds (It offends me that the cliff height has 4 sig figs, and we use a g of 10 m/s² - just saying!)

The d that lorry travels is vt_air for constant velocity and for the lorry to be at the same x coordinate at the time that the stone hits the ground.

v = d/t_{air = 75 m/(6.242 s) = 12 m/s 12.02)}

_{The distance that the truck goes is the same as the horizontal range of a horizontally launched projectile with the initial velocity equal to the truck's.}