Answer to Question #176872 in Physics for Francine

Question #176872

 An object has a launch velocity of 30.0 m/s at launch angle of 30.00relative to  

horizontal. Find the a) x and y component of initial velocity, b) time to reach the peak  

c) total time of flight, d) vertical height to reach the peak, and e) horizontal distance.




1
Expert's answer
2021-03-31T12:52:37-0400

a) The horizontal (x) component of the velocity is:


vx=30m/scos30°=153m/s13m/sv_x = 30m/s\cdot \cos30\degree = 15\sqrt3 m/s\approx 13m/s

The vertical (y) component of the velocity is:


vy=30m/ssin30°=15m/sv_y = 30m/s\cdot \sin30\degree = 15m/s

b) Time to reach the peak can be found as follows (https://en.wikipedia.org/wiki/Projectile_motion):


tmax=vsinθg=30m/ssin30°9.8m/s21.53st_{max} = \dfrac{v\sin\theta}{g} = \dfrac{30m/s\sin30\degree}{9.8m/s^2} \approx 1.53s

where g=9.8m/s2g = 9.8m/s^2 is the gravitational acceleration.

c)  The total time of flight is:


ttot=2tmax3.06st_{tot} = 2t_{max}\approx 3.06s

d) Vertical height to reach the peak is:


hmax=v22g=(30m/s)229.8m/s245.9mh_{max} = \dfrac{v^2}{2g} = \dfrac{(30m/s)^2}{2\cdot 9.8m/s^2}\approx 45.9m

e) Horizontal distance is:

dtot=v2sin2θg=(30m/s)2sin60°9.8m/s279.5md_{tot} = \dfrac{v^2\sin2\theta}{g} = \dfrac{(30m/s)^2\sin60\degree}{9.8m/s^2} \approx 79.5m

Answer. a) 13m/s, 15m/s. b) 1.53s, c) 3.06s, d) 45.9m, e) 79.5m.


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