# Warm-Up Exercise for lecture 4

## Due 8:00 am, Thurs, Sep 11

Physics 105, Fall 2008

I throw a ball at an upward angle across a flat field. Neglecting air resistance, at what part of its path does the ball have its maximum speed?
☑ right before it hits the ground
☐ halfway to the top
☐ at the top of its path
☐ right after it leaves my hand
☐ There's not enough information to say

Neglecting air resistance, at what angle should you throw a ball on a flat field in order to get the maximum range?
☐ 30°
☑ 45°
☐ 60°
☐ It depends on the initial speed

Object 1 is thrown upwards with an angle of 30° with respect to the horizontal. Object 2 is thrown upwards with the same speed, but at 60°. Neglecting air resistance, which object stays in the air longer?
☐ Object 1
☑ Object 2
☐ They stay in the air the same time
☐ It can't be determined from the information given

Ralph asked me a question the other day. Consider a ball which is thrown upwards at an angle. Ralph thought that since the ball is still moving upwards for a while after it is thrown, it must have some upwards acceleration in the air after it leaves my hand that continues to propel the ball. I told him "No, that's not quite what is happening." Can you help Ralph understand what is happening?

My hand has imparted some initial *velocity* to the ball, but after it leaves my hand, my hand no longer affects the ball's motion at all. At that point, the ball is in free-fall, and accelerates downwards due to gravity. Because of the initial velocity, it takes some time for the downwards acceleration to slow the ball down and start it coming back to earth. But it is accelerating downwards the whole time after it leaves my hand.