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Example Problems:
2) What is the total time in flight of the rocket?
The formulas we need to solve this problem are the following:
• u
x
= u0 • cosθ
• u
y
= u0 • sinθ – (g • t)
t at the time of launch is t1 which = 0
t at the time the rocket lands (ground) is t2. At t2, y = 0.
Therefore, if y = u • t • sinθ – 0.5gt2:
y = t(u • sinθ – 0.5gt) or y = 2(u • sinθ) – gt
At t2, y = 0, so 2(u • sinθ) – gt = 0
t = 2(u • sinθ) / g
t2 = 2(25 • sin 30) / 9.8
t2 = 2.55 sec
so time of flight = t2 – t1 = 2.55 – 0 = 2.55 seconds
3) What is the horizontal range (distance covered) of the rocket?
The formulas we need to solve this problem are the following:
• x = u • t • cosθ
So in this case, we are looking for x at t2 – t1 (which is 2.55 seconds from part b)
x = 25 • 2.55 • cos 30 = 32.3 meters
4) What is the magnitude of the velocity of the object just before it hits the ground?
The formulas we need to solve this problem are the following:
• u
x
= u0 • cosθ
• u
y
= u0 • sinθ − (g • t)
• u = √(u2 x + u2 y)
We are solving for the velocity components at t2 = 2.55 seconds
u
x
= u0 • cosθ u
x
= 25 (cos 30) = 23.5 m/s
u
y
= u0 • sinθ − (g • t) u
y
= 25 (sin 30) – (9.8 • 2.55) = - 12.5 m/s
u = √(u2 x + u2 y) u = √(23.5)2 + (-12.5)2 = 26.6 m/s