Question

Show your work. Circle your answer.

3) An artillery shell is fired with an initial velocity of 318 m/s at 64° above the horizontal. It explodes on a mountainside 43 s after firing. What are the x and y coordinates of the shell where it explodes, relative to its firing point?

Answer 1

Answer 2

SOLUTION :

Shell is fired at an angle of 64º and speed of 318 m/s. 

upward. It travels for 43 seconds and explodes.

So, 

horizontal speed  of shell , Vh = 318 cos (64) =  139.4020 m/s

vertical speed  of shell  , Vv = 318 sin (64) = 285.8165  m/s

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

X - coordinate of shell at explosion point 

= Horizontal distance moved by shell 

= Horizontal speed * time 

= 139.4020 * 43

 = 5994.29 meters  (ANSWER)

Y-coordinate of shell at explosion point 

= vertical distance travelled by shell 

= u t - 1/2 g t^2   ;  (u = Vv)

= (285.8165)(43) - 1/2 * 9.8 * (43)^2 

= 3230.00  meters. (ANSWER).