Projectile Motion Question (1 Viewer)

[凍鴛鴦]

Hi all,

A ball is thrown from a point on a horizontal plane with an initial velocity of 25 m/s at an angle of 40 degrees to the horizontal. Taking g = 10m/s^2 calculate:

(c) the speed with which it strikes the ground

The answer says 25m/s, but I don't think it is. Yes, the horizontal component would be 25m/s but the overall velocity is not 25m/s when it strikes the ground???

Any help greatly appreciated, thanks!

 

[acmilan]

x = 25tcos40

y = 25tsin40 - 5t²

when it hits the ground, y = 0

25tsin40 - 5t² = 0

t = 0 or t = 5sin40

When t = 5sin40:

y' = 25sin40 - 10t = 25sin40 - 50sin40 = -25sin40

x' = 25cos40

Now to work out velocity you draw the triangle and use pythagoras/trig ratios

You get: V² = (25cos40)² + (-25sin40)² -> V = 25 m/s

 

[word.]

Hello Frozen Duck.

On an even horizontal plane, the initial velocity of a projectile = its final velocity.
The question does not say that the initial horizontal velocity is 25m/s, it says the initial overall velocity is 25m/s. This means that the horizontal velocity is 25cos40° m/s however is not required for this part of the question.

 

[凍鴛鴦]

Thanks for the quick responses! I understand acmilan's answer. However, I don't understand logically why the final velocity would equal the initial velocity? Doesn't the velocity decrease by -g due to acceleration over the course of the flight?

Edit Oops I get it now. It's because the gravity decreases the velocity as it gets up the the max, and then it increases its velocity again as it falls down. Thanks anyway =D

Edit 2 Oh and another question, is it possible to do this question using a cartesian way instead of parametrically?

 

[damo676767]

to get the cartesian equation you need to us parametrics

 

[mattchan]

+ a parabola is symmetrical, so initial velocity = final velocity on a flat horizontal plane.

 

[Riviet]

You could probably do it by breaking it into its vertical and horizontal motion and then calculate stuff like horizontal velocity and vertical velocity keeping in mind that g does not affect horizontal velocity. Then you can form a triangle and work out the the velocity as it hits the ground.