1. a soccer ball is kicked at an upward angle θ between 0° and 90°. its initial vertical (y) velocity vy0 is 19.6 m/s. it follows a parabolic trajectory and lands at the end of its range. c. if the ball’s range is 60 m, is the angle θ less than, equal to, or greater than 45°? 2. a small toy car is placed upon a ramp that is 2 m long. the car is released (with zero initial velocity) from the top of the ramp. assume that friction is negligible.(aramp= 1 m/s2) how high is the top if the car takes 2.0 s to reach the bottom?

#1

As the ball is projected at some angle with vertical speed

now we can find the time of flight

now we can find the horizontal speed as

Range = horizontal speed * time

now for the projection angle we will have

so here angle is more than 45 degree as the above ratio is more than 1

#2

here we know that car takes t = 2 s to reach the bottom

here acceleration = 1 m/s^2

initial speed = 0

we can use kinematics now

so the toy car is released from the top at distance 2 m from the bottom

32: from largest to smallest, this hierarchy includes eons, eras, periods, epochs, and ages.

33: answer is c

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