A toy gun on a horizontal surface fires a bullet at 70° above the horizontal. If the bullet has an initial velocity of 39 m/s and feels negligible air resistance, after how long does the bullet reach the highest point in its trajectory?

The study of animal jumps is common in the academic discipline. The jumps are often reported in multiples of body length. Grasshoppers have attained maximum heights of 95.2 cm above the ground. If a grasshopper leaps at 54.0° above the horizontal, determine the takeoff speed for the leap.

From sea level, an archer stands on the edge of a cliff that is 20 m above the ground. He fires an arrow with a speed of 70 m/s at an angle of 58° above the horizontal. Draw the x-t, y-t, u_x-t, and u_y-t graphs for the motion of the arrow upon shooting. Ignore air resistance.

Astronauts are on a space mission to do research work. As a part of this mission, they throw a projectile on an unknown planet which follows the projectile path shown below. The projectile's status at an interval of 2 s is shown from 0 s to 6 s. The ball's velocity at t = 2 s is v = (3.0 i + 5.0 j). Calculate the velocity of the projectile at t = 0 s, 4 s, 6 s.

Some boys are playing basketball. One boy shoots the ball towards the basket at a height of 'h' from the ground. The ball has a takeoff speed of 12 m/s and a launch angle of 50° above the horizontal. The ball passes through the basket after 3.0 s. Determine the largest vertical displacement experienced by the ball.

An archer aims to hit a target on a tower, with the center of the target being 18.0 m above the ground and 50.0 m away horizontally as shown. The archer releases the arrow from a height of 1.5 m. To ensure the arrow hits the target with a purely horizontal velocity component for a precision strike, what must be the horizontal speed of the arrow as it hits the target?