Physics Help

Question

Samantha fires a rubber band from a balcony 20m high at an angle of 30° above the horizontal. It strikes the ground 10.4s later.

 

a) Find the initial speed

 

b) Find the magnitude and direction of the velocity vector after 7s.

 

c) With the balcony as the origin, find the x and y coordinates of the highest point of the motion.

Answer 1

This problem become much easier if you break it up into x and y directions.

First list every thing about the x direction

t = 10.4s

v_(x) = v_(i)cos(theta)

 

Then the y direction

t = 10.4s

change in y = -20 m

a = -9.8m/s/s

v_(i)y = v_(i)sin(theta)

 

A) You have enough information to calculate the initial y velocity using:

change y = v_(i)yt + 1/2at²

 

Once you have v_(i)y, you can solve for v(i) using v(i)y = v(i) sin (theta)

 

B) Since the horizontal velocity never changes, solve for v(x) using v(x) = V(i) cos (theta)

Then solve for the y velocity after 7s using vf = vi +at.  This will give you the y component of that velocity.

 

You will then need to solve the triangle for the hypotenuse.  This is the combined velocity.  Solve the triangle for an angle to give the direction.

 

C) Solve for the time it takes for the vertical velocity to reach zero using vf = vi +at.  With that time solve for the y component of height by using vf² = vi² + 2a(change in y).  Then use the time to solve for the horizontal distance using V = (change in x)/t.