A fireworks show is choreographed to have two shells cross paths at a height of 138 feet and explode at an apex of 175 feet under normal weather conditions. The shells have a launch angle = 61° above the horizontal. If a strong wind induces a constant rightward acceleration of 16 ft/sec² for the fireworks shells, determine the horizontal shift Ax of the crossing point of the shells.

Goro Shigeno (Pitcher) and Joe Gibson Jr. (hitter) went head to head in the Major League Baseball (MLB) series. For the last pitch, Gibson hits the baseball with 82 ft/s at angle of 75°. When the ball is directly above Shigeno he begins to run under it. Determine the (a) the total distance that the pitcher runs and (b) the constant speed at which pitcher must run in order to make the catch at the same elevation at which the ball was hit. (Note: the distance between the pitcher and hitter is 70 ft.)

In my homework, I am asked to derive an equation for V0.   The homework question is as follows: A howitzer fires a shell with a velocity of v0 at an angle Θ above the horizontal. The howitzer is on a plateau and the shell lands down in the plain below, a vertical distance d below the plateau and a horizontal distance L from where the howitzer is. Derive an expression for the magnitude of the initial velocity, V0, as a function of d, L, g, and Θ.   Any help would be appreciated as I have worked on this problem for quite a while and I am not making progress.

2 M S F2 7. The captain of a small plane starts his journey by proceeding west. The speed of the plane with respect to still air is 170 km/h. A sudden south wind starts to blow at a constant speed of 87.5 km/h. What is the speed of the plane relative to the ground if no action is taken by the pilot? km/h 3 8. b) As seen by people on the ground, what is the angle made between the direction of motion of the plane with repect to the west? 9. c) At what angle with respect to the west must the pilot head his plane in order for it to proceed west as seen by the people on the ground? E 80 F3 D $ 4 F4 R F % O 5 F5 T G 6 MacBook Air IS Y & 7 H F7 U * 8 J DII FB ( 9 K F10 L P F12

You are designing a missile defense system that will shoot down incoming missiles that pass over a perimeter defense post. The set-up is shown below. An incoming missile passes directly above the defense base. Radar at the base can measure the height, h, and speed, v1, of the incoming missile. Your Patriot Rocket is set to fire at an angle of θ=67∘ from vertical. You design the Patriot Rocket so the magnitude of its acceleration is given by: a2=Ae^−bt where A can be set on your Patriot Rocket as it is fired, b=0.15 s−1, and t=0 s when it is fired. The direction of your Patriot Rocket's vector acceleration stays at the same angle, θ, for the entire trip. If an incoming missile passes over the defense base at a height of 4.7 km and at a constant speed of 757 m/s (this means that v→1 is constant), solve for the value of A your Patriot Rocket must have in order to hit the incoming missile. You will also need to enter results from intermediate steps of your calculation, including the…

You are designing a missile defense system that will shoot down incoming missiles that pass over a perimeter defense post. The set-up is shown below. An incoming missile passes directly above the defense base. Radar at the base can measure the height, ℎ, and speed, v1, of the incoming missile. Your Patriot Rocket is set to fire at an angle of θ=70∘ from vertical. You design the Patriot Rocket so the magnitude of its acceleration is given by: a2=Ae^(-bt) where A can be set on your Patriot Rocket as it is fired, b=0.3 s−1, and t=0 s when it is fired. The direction of your Patriot Rocket's vector acceleration stays at the same angle, θ, for the entire trip. If an incoming missile passes over the defense base at a height of 4.4 km and at a constant speed of 797 m/s (this means that vector v1 is constant), solve for the value of A your Patriot Rocket must have in order to hit the incoming missile. You will also need to enter results from intermediate steps of your calculation, including the…