Question

An artillery shell is red with an initial velocity of 328 m/s at 51.1 degrees above the

horizontal. To clear an avalanche, it explodes on a mountainside 42.1 s after firing. What

are the (a) x and (b) y coordinates of the shell where it explodes, relative to its firing

point? What are the (c) x and (d) y components of its velocity just before it hits the

mountainside? Be sure to include the correct sign on the answers.

Answer 1

the horizontal compontent of velocity = 328 cos (51.1) = 205.97 m/s

after 42.1 s it is at a distance of 205.97*42.1 = 8671.42 m

the vertical component of velocity = 328 sin (51.1) = 255.26 m/s

the acceleration due to gravity = 9.8 m/s downward

so the distance travelled in 42.1 s = ut+0.5at*t

= 255.26 * 42.1 -0.5*9.8*42.1*42.1

=2061.8 m

so the components of position

x co ordinate = 8671.42 m

y co ordinate = 2061.8 m

now the horizontal velocity remains same = 205.97

as there is no acceleration in the horizontal direction

the vertical component changes as there is acceleration in downward direction

final velocity = u+at = 255.26 + (-9.8)*42.1 = -157.37

so x component of velocity = 205.97 m/s

y component = -157.37 m/s