Hey!(adsbygoogle = window.adsbygoogle || []).push({});

I always had a few difficulties with projectile motion problems, so I just solved one and I wanted to verify if my solution is ok, since I don't have a book with solutions so I can't check if I understood the problem well....

So it's about somebody on a bike who rides off an entrenchment (that's what it's called right?) with a velocity v under an angle of alpha with the ground. He's hoping to land safely on another entrenchement that's h heigher than the first one, at a distance x from the first entrenchment:

For a given height h, find the minimal velocity vmin the jumper needs to have in order to land safely on the platform at a distance x.

Well what I did is the following:

The well known formula's for the projectile motion are:

x(t)= v0x t + x0

y(t)= y0 + v0y t - 1/2 gt^2

Where v0x= v0 cos @ and v0y= v0 sin @

So if x(t)= x than y(t)= h.

x= v0x t and h= v0y t - 1/2 gt^2

Therefore t= x/v0x. Substitution in the h formula gives:

h= ((v0y x)/v0x)- 1/2 g (x/v0x)^2= ((v0y x)/v0x)- (g x^2)/(2 v0x^2)

Knowing v0x= v0 cos @ and v0y= v0 sin @ substitution gives:

h= ((x v0 sin@)/ v0 cos @) - (g x^2)/ (2 v0^2 (cos^2)@)

h= x tan @ - (g x^2)/ (2 v0^2 (cos^2)@)

(g x^2)/ (2 v0^2 (cos^2)@)= x tan@ -h

(2 v0^2 (cos^2)@)= (g x^2)/ (x tan@-h)

v0^2= (g x^2)/ (2 (cos^2)@ (x tan@ -h))

v0= sqrt((g x^2)/ (2 (cos^2)@ (x tan@ -h)))

Is this correct?! Thanks in advance for your effort!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Projectile motion problem

**Physics Forums | Science Articles, Homework Help, Discussion**