The horizontal and vertical components of the initial velocity of a projectile are 64.6 m/s and 82.7 m/s, respectively. If it is projected from a height of 65 m above the ground, how long does it take the projectile to rise the highest point of its trajectory?[Assume that g = 9.8 m/s*).

A skateboarder shoots off a ramp with a velocity of 7.9 m/s, directed at an angle of 51° above the horizontal. The end of the ramp is 1.4 m above the ground. Let the x axis be parallel to the ground, the +y direction be vertically upward, and take as the origin the point on the ground directly below the top of the ramp. (a) How high above the ground is the highest point that the skateboarder reaches? (b) When the skateboarder reaches the highest point, how far is this point horizontally from the end of the ramp? (a) Number_____  Units_____                                                            (b) Number ____  Units ____

A ball is kicked with an initial velocity of 16 m/s in the horizontal direction and 12 m/s in the vertical direction. The ball lands a horizontal distance of 50 m from where it was kicked. (a)  For how long does the ball remain in the air? (b)What maximum height is attained by the ball?

A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of v0 = 17.5 m/s. The cliff is h = 32.0 m above a flat, horizontal beach as shown in the figure. (a) What are the coordinates of the initial position of the stone? x0     m y0     m (b) What are the components of the initial velocity? v0x     m/s v0y     m/s (c) Write the equations for the x- and y-components of the velocity of the stone with time. (Use the following as necessary: t. Let the variable t be measured in seconds. Do not include units in your answer.) vx   vy   (d) Write the equations for the position of the stone with time, using the coordinates in the figure. (Use the following as necessary: t. Let the variable t be measured in seconds. Do not state units in your answer.) x   y   (e) How long after being released does the stone strike the beach below the cliff? (f) With what speed and angle of impact does the stone land? vf    m/s θ…