Step-by-step solution
Use trigonometry to determine the x and y components of the initial velocity from the initial speed and the angle.
Now we focus on the vertical dimension of motion, using the initial y velocity to determine the time the cannonball is in the air. We calculated
the initial y velocity in step 3.
Now we use the time and the x velocity to solve for the cannonball’s range. We calculated the constant x velocity in step 6.
Step Reason
1. vy = v sin ș trigonometry
2. vy = (40.0 m/s) sin 60.0° enter values
3. vy = 34.6 m/s evaluate
4. vx = v cos ș trigonometry
5. vx = (40.0 m/s) cos 60.0° enter values
6. vx = 20.0 m/s evaluate
Step Reason
7. vyf = vyi + ayt linear motion equation
8. ívyi = vyi + ayt final y velocity is negative of initial y velocity
9. í^2 vyi = ayt rearrange
10. solve for time
11. enter values
12.t = 7.07 s evaluate
Step Reason
13. definition of velocity
14.ǻx = vxt rearrange
15.ǻx = (20.0 m/s)(7.07 s) enter values
16.ǻx = 141 m multiply
Copyright 2000-2007 Kinetic Books Co. Chapter 04^77
