One strategy in a snowball fight is to throw a snowball at a high angle over level ground. Then while your opponent is watching that snowball, you throw a second one at a low angle timed to arrive before or at the same time as the first one. Assume both snowballs are thrown with a speed of 25.0 m/s. The first is throw at an angle of 70.0o with respect to the horizontal. a)  At what angle should the second snowball be thrown to arrive at the same point as the first? Assume air resistance is negligible. b)  How many seconds later should the second snowball be thrown after the first for both to arrive at the same time?

A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of vi = 18.0 m/s. The cliff is h = 50.0 m above a body of water as shown in Figure P4.13. (a) What are the coordinates of the initial position of the stone? (b) What are the components of the initial velocity of the stone? (c) What is the appropriate analysis model for the vertical motion of the stone? (d) What is the appropriate analysis model for the horizontal motion of the stone? (e) Write symbolic equations for the x and y components of the velocity of the stone as a function of time. (f) Write symbolic equations for the position of the stone as a function of time. (g) How long after being released does the stone strike the water below the cliff? (h) With what speed and angle of impact does the stone land? Figure P4.13

A basketball player is standing on the floor 10.0 m from the basket as in Figure P3.47. The height of the basket is 3.05 m, and he shoots the ball at a 40.0 angle with the horizontal from a height of 2.00 m. (a) What is the acceleration of the basketball at the highest point in its trajectory? (b) At what speed must the player throw the basketball so that the ball goes through the hoop without striking the backboard?

A World War II bomber flies horizontally over level terrain with a speed of 275 m/s relative to the ground and at an altitude of 3.00 km. The bombardier releases one bomb. (a) How far does the bomb travel horizontally between its release and its impact on the ground? Ignore the effects of air resistance. (b) The pilot maintains the planes original course, altitude, and speed through a storm of flak. Where is the plane when the bomb hits the ground? (c) The bomb hits the target seen in the telescopic bombsight at the moment of the bombs release. At what angle from the vertical was the bombsight set?

A projectile is launched at an angle of 30 and lands 20 s later at the same height as it was launched. (a) What is the initial speed of the projectile? (b) What is the maximum altitude? (c) What is the range? (d) Calculate the displacement from the point of launch to the position on its trajectory at 15 s.

Two birds begin next to each other and then fly through the air at the same elevation above level ground at 22.5 m/s. One flies northeast, and the other flies northwest. After flying for 10.5 s, what is the distance between them? Ignore the curvature of the Earth.

A rugby player passes the ball 7.00 m across the field, where it is caught at the same height as it left his hand. (a) At what angle was the ball thrown if its initial speed was 12.0 m/s, assuming that the smaller of the possible angles was used? (b) What other angle gives the same range, and why would it not be used? (c) How long did this pass take?

MIT’s robot cheetah can jump over obstacles 46 cm high and has speed of 12.0 km/h. (a) If the robot launches itself at an angle of 60 at this speed, what is its maximum height? (b) What would the launch angle have to be to reach a height of 46 cm?

Prove that the trajectory of a projectile is parabolic, having the form y=ax+bx2. To obtain this expression, solve the equation x=v0xt for t and substitute it into the expression for y=v0yt(1/2)gt2 (These equations describe the x and y positions of a projectile that starts at the origin.) You should obtain an equation of the form y=ax+bx2 where a and b are constants.

The same vectors that are shown in Figure P3.6 are shown in Figure P3.42. The magnitudes are F1 = 1.90f, F2 = f, and F3 = 1.4f, where f is a constant. a. Use the coordinate system shown in Figure P3.42 to find R=F1+F2+F3 in component form in terms of f. b. If Rx = 0.33, what is Ry? c. Check your result by comparing your answer to that of Problem 6. FIGURE P3.42