(B) How long does it remain in flight? Analyze The y-component of the projectile

Question

(B) How long does it remain in flight?

Analyze
The y-component of the projectile's velocity decreases by 9.8 m/s for each second of flight as the projectile rises. Therefore it takes a time of

ty,max = vyi
g
= vi sin ?
g


for the vertical component of velocity to reach a value of 0, which occurs at the projectile's maximum height. At each height on the way down the particle has regained the same speed and has the same acceleration as it had on the way up, so that the complete time of flight is twice the time to reach the maximum height, and is equal to
tflight = 2vi sin ?
g


In the present problem, that expression gives
tflight = 4 s

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(C) For a given launch speed, what launch angle produces the longest time of flight?
Analyze
The time of flight for a given initial speed vi,

tflight = 2vi sin ?
g


is largest when sin ? is largest, which is at ? = 5 °. What does that correspond to physically?

Explanation / Answer

the time of fight is maximum for 45 degrees because sinx is maximum at 45 degrees

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