Answer to Question #292544 in Mechanics | Relativity for Nash

Question

A stone is thrown from a point A with speed 27 m/s at an angle of 26 degree below the horizontal. The point A is 25 m above the horizontal ground. Find the horizontal range of the stone in meter. Give your answer with one decimal place.

Answer 1

Solution

Speed in horizontal direction

$u_x=27\times cos26°= 24.27m/s\\u_y=27\times sin26°=11.84m/s$

Height from plane

H=-25m

So using second equation of motion

$-25=11.84t-4.9t^2$

$t^2-2.42t-5.1=0$

SO solutions of this quadratic equation is that

$t=\frac{2.42±\sqrt{5.86+20.4}}{2}\\=\frac{2.42±\sqrt{26.26}}{2}\\=\frac{2.42±5.12}{2}$

Using plus sign

t =3.77sec.

So horizontal range is

R=$24.27\times3.77=91.50m$