Two projectiles are l aunched simultaneously from the same point on a horizontal

Question

Two projectiles are launched simultaneously from the same point on a horizontal surface, one at 45 to the horizontal and the other at 60. Their launch speeds are different and are chosen so that the two projectiles travel the same horizontal distance before landing. Suppose the 45projectile is launched with speed v and that it's in the air for time t.

A) Find expression for the launch speed of the 60 projectile.

Express your answer in terms of v.

B) Find expression for the flight time of the 60 projectile.

Express your answer in terms of t.

Explanation / Answer

Formula to be used:
time of flight of projectile:
t = (2Vo sin thetha)/g

Range of projectile,
R = Vo^2 * sin (2*thetha) / g

A)
For both projectile, R is same
so,
R1=R2
V1o^2 * sin (2*thetha1) / g = V2o^2 * sin (2*thetha2) / g
v^2 * sin(2*45) =V2o^2 * sin(2*60)
v^2*1= V2o^2*0.866
1.15 v^2 = V2o^2
V2o =1.07 v
Answer: 1.07 v

B)
Time of flight of 45 o projectile:
t= (2Vo sin thetha)/g
= 2* v*sin 45 / g
=2*v*sin45 / 9.8
= 0.1443 v

Time of flight of 2nd projectile,
t2= (2 V2o sin thetha2)/g
= (2* 1.07v*sin 60 )/ 9.8
= 0.189 v
but v = t/0.1443
so,
t2= 0.189*t/0.1443
=1.3 t
Answer: 1.3 t

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