Question

An artillery shell is fired with an initial velocity of 300 m/s at 51.0° above the horizontal. To clear an avalanche, it explodes on a mountainside 42.5 s after firing. What are the x- and y-coordinates of the shell where it explodes, relative to its firing point?

Answer 1

Initial Horizontal and vertical components of velocities

V_ox=300Cos51

V_oy=300Sin51

Horizontal distance traveled

X=V_oxt =(300Cos51)(42.5)

X=8023.83 m

From

Y=Y_o+V_oyt-(1/2)gt²

Y=0+(300Sin51)(42.5)-(1/2)(9.81)(42.5)²

Y=1048.95 m

Answer 2

SOLUTION :

Shell is fired at an angle of 51º and speed of 300 m/s. 

upward. It travels for 42.5 seconds and explodes.

So, 

horizontal speed  of shell , Vh = 300 cos (51) =  188.7961 m/s

vertical speed  of shell  , Vv = 300 sin (51) = 233.1438 m/s

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

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

= 188.7961 * 42.5 = 8023.83 meters 

Y = vertical distance travelled by shell 

= u t - 1/2 g t^2   ;  (u = Vv)

= (233.1438)(42.5) - 1/2 * 9.8 * (42.5)^2 = 1057.99  meters.

Hence, X, Y coordinates of explosion point are : 8023.83 m and 1057.99 m respectively.

(ANSWER).