Projectile Motion

[NYKnick]

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A projectile is launched from a 25m platform at an angle of 30C to the horizontal. Its initial velocity is 40 m/s. How long is it in the air?

a: 2s
b: 3s
c: 4s
d: 5s

I chose 4s, EK says its 5s but it doesn't do a good job explain so.

 

[Majik]

First I found the total height (ie. height to peak from floor):

The initial vertical velocity is: 20 m/s (40sin30)
The final vertical velocity (at peak) is: 0m/s
The average velocity is therefore: 10m/s

It takes 2 seconds to reach the peak (t=deltaV/acceleration). Therefore the distance to peak is, d=Vavg x t; d=(10m/s)(2s) = 20m

I added 20m to 25m (platform height) = 45m (height at peak)

Then using this equation: d=vit + 1/2at^2, I solved for time.
At this point the initial velocity is 0 since it's falling (ie. it starts at the peak).
d=1/2at^2 ==> t^2 equals: (45m)(2)/(10m/s^2) = 9

The square root of 9 is 3, therefore it takes 3 seconds to fall down. But this is the time it takes to fall down, we didn't include the time it takes to reach its peak. Earlier I mentioned it takes 2 seconds to reach it's peak.

Therefore the total time is: 2s + 3s = 5s

 

[NYKnick]

Bro that was really good! conceptually i understood why the answer is above 4 secs.. i just couldn't understand why it was 5 and not any number greater than 4.

 

[muhali3]

For the exact answer, this is what you would have to do:

First, calculate time to reach max height:

Tmaxheight = Viy/g = 20/10 = 2 seconds

This is the time it takes for the first half of parabolic motion. Since parabolic motion is symmetric, the second half also takes 2 seconds.

2 seconds + 2 seconds = 4 seconds (to return back to 25m above ground)

So at 4 seconds, it is 25m above the ground. Now you have to calculate how long it will take to fall.

Use this formula: x = Vit + 1/2at^2

At 4 seconds, the ball is going 20m/s downwards (2s x g), so:

25 = 20t + 1/2gt^2

Solve for t with the quadratic formula:

t^2 + 4t - 5 = 0

t = 1 or -5

Time can only be positive, so t = 1

So the answer is: 2 seconds + 2 seconds + 1 seconds = 5 seconds

 

[NYKnick]

I got it the first time but I appreciate the further explanation.

 

[muhali3]

just wanted to give you a different perspective.

 

[NYKnick]

Thanks