Question

An artillery shell is fired with an initial velocity of 300 m/s at 48.0° above the horizontal. To clear an avalanche, it explodes on a mountainside 37.0 s after firing. What are the x- and y-coordinates of the shell where it explodes, relative to its firing point?

x=?

y=?

Answer 1

Answer 2

SOLUTION :

Shell is fired at an angle of 48º and speed of 300 m/s. 

upward. It travels for 37 seconds and explode.

So, 

horizontal speed  of shell , Vh = 300 cos (48) =  200.7392 m/s

vertical speed  of shell  , Vv = 300 sin (48) = 222.94345 m/s

Coordinates of explosion point relative to firing point(0, 0) :

X = Horizontal distance moved by shell = Horizontal speed * time 

= 200.7392 * 37 = 7427.35 meters 

Y = vertical distance travelled by shell 

= u t - 1/2 g t^2   ;  (u = Vv)

= (222.94345)(37) - 1/2 * 9.8 * (37)^2 = 1540.81 meters.

Hence, X, Y coordinates of explosion point are : 7427.35 m and 1540.81 m respectively.

(ANSWER).