Two projectiles are thrown with the same initial speed one

Question

Question 1: Two projectiles are thrown with the same initial speed, one at an angle θ with respect to the level ground and the other at angle 90^o - θ. Both projectiles strike the ground at the same distance from the projection point. Are both projectiles in the air for the same length of time?

Question 2: A projectile is launched at some angle to the horizontal with some initial speed v_i, and air resistance is negligible. (a) Is the projectile a freely falling body? (b) What is its acceleration in the vertical direction? (c) What is its acc ration in the horizontal direction?

Question 3: An artillery shell is fired with an initial velocity of 300 m/s at 55.0° above the horizontal. To clear an avalanche, it explodes on a mountainside 42.0 s after firing. What are the x- and y-coordinates of the shell where it explodes, relative to its firing point?

Question 4: A projectile is launched with an initial speed of 60.0 m/s at an angle of 30.0° above the horizontal. The projectile lands on a hillside 4.00 s later. Neglect air friction. (a) What is the projectile's velocity at the highest point of its trajectory? (b) What is the straight-line distance from where the projectile was launched to where it hits its target?

Question 5: A rocket is launched at an angle of 53.0° above the horizontal with an initial speed of 100 m/s. The rocket moves for 3.00 s along its initial line of motion with an acceleration of 30.0 m/s2. At this time, its engines fail and the rocket proceeds to move as a projectile. Find (a) the maximum altitude reached by the rocket, (b) its total time of flight, and (c) its horizontal range.

Question 6: The equation of a parabola is y = ax² + bx + c, where a, b, and c are constants. The x- and y-coordinates of a projectile launched from the origin as a function of time are given by x = v_0xt and y = v_0yt - 1/2gt², where v_0x and v_0y are the components of the initial velocity. (a) Eliminate t from these two equations and show that the path of a projectile is a parabola and has the form y = ax + bx². (b) What are the values of a, b, and c for the projectile?