A cannonball is fired from a cliff top horizontally out to sea with a speed of 74m/s. The cliff is 320m above sea level. Calculate the speed of impact?

how do you calculate the speed of impact pls help!!

1 Answer
Steve J.
Nov 1, 2017

#"speed of impact" = 108 m/s#

Explanation:

The question does not say anything about air resistance, so we are to ignore air resistance. This simplifies the problem significantly.

Therefore the cannonball's horizontal velocity, #v_h#, continues without change. It gains velocity in the vertical direction according to the suvat formula

#v^2 = u^2 + 2*a*s " "# where

  • u = 0 because the cannonball is fired horizontally
  • #a = 9.8 m/s^2#
  • and s = 320 m.

Filling the data into that formula will give us the final vertical velocity, #v_v#.

#v_v^2 = 0^2 + 2*9.8 m/s^2*320 m = 6272 m^2/s^2 #
#v_v = sqrt(6272 m^2/s^2) = 79.2 m/s #

The cannonball's speed of impact is the magnitude of its final velocity. The final velocity will be the vector sum of its #v_h# and #v_v#.

#"speed of impact" = sqrt(v_h^2 + v_v^2)#
#"speed of impact" = sqrt((74m/s)^2 + (79.2 m/s)^2)#
#"speed of impact" = sqrt(11,748 m^2/s^2) = 108 m/s#

I hope this helps,
Steve

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