Three vectors are shown in Figure. Their magnitudes are given in arbitrary units

Question

Three vectors are shown in Figure. Their magnitudes are given in arbitrary units. Determine the sum of the three vectors. Give the resultant in terms magnitude and angle with x axis. A projectile is shot from the edge of a cliff 115 m above ground level with an initial speed of 65.0 m/s at an angle of 30.0 degree with the horizontal. Determine the time taken by the projectile to hit the ground level. Determine the distance X from the base of the vertical cliff to the point the projectile hit the ground.

Explanation / Answer

We will neglect air resistance.
The initial vertical velocity is 65sin30 = 37.28 m/s
as velocity is acceleration by time and the vertical acceleration is g = 9.81 m/s/s
the time to peak point is found by
V = at
37.28 = 9.81t
t = 37.28 / 9.81 = 3.8 seconds

the height reached above the launch point is at 3.8 seconds
h = 1/2at^2
h = 1/2 (9.81)(3.8^2)
ANS f) h = 70.84 m

so the total drop from apex is 115 + 70.84 = 185.84 m
again using h = 1/2at^2 only this time to solve for t
185.84 = 1/2(9.81)t^2
t^2 = 37.89
t = 6.16 seconds
ANS a) total time in flight 6.16 + 3.8 = 9.96 seconds

the horizontal initial velocity never changes from 65cos35 = 53.24 m/s

ANS b) the horizontal distance is 53.24(9.96) = 530 m

the total straight line distance from the cliff top launch point is (530^2 + 115^2)^0.5 = 542.4 m


the vertical velocity component at landing will be
9.81(6.16) = 97.7 m/s


Taking 30 instead of 35, working on it

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