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- Olympus Mons on Mars is the largest volcano in the solar system, at a height of 25 km and with a radius of 312 km. If you are standing on the summit, with what Initial velocity would you have to fire a projectile from a cannon horizontally to clear the volcano and land on the surface of Mars? Note that Mars has an acceleration of gravity of 3.7m/s2 .A projectile was fired at an angle of 30.0° above the horizontal with an initial speed of 20 m/s. The same projectile was fired a second time with the sane initial speed of 20 m/s but at a different angle such that the height attained by the projectile in the second launch is one half of the horizontal distance covered by the projectile in the first launch. At what angle was the projectile launched second time?At what angle with the horizontal should a hunter aim his gun so he will hit a target which is 60m horizontally away from him and 20 m above him, if the muzzle velocity of the bullet is 400 m/s
- If you are standing on the free-throw line on a basketball court, the basket is about 4.5 m horizontally from you and it is located around 3m above the floor. What initial velocity vector is required to successfully throw the ball into the basket?An archer fish spies a meal of a grasshopper sitting on a long stalk of grass at the edge of the pond in which he is swimming. The fish is to successfully spit at and strike the grasshopper, which is 0.200 m away horizontally and 0.335 m above his mouth. What is the minimum speed at which the archer fish must spit?A projectile is fired with an initial speed of 40 m/s at angle of 23 degrees above the horizontal on a long flat firing range. Determine (1) the maximum vertical distance reached by the projectile, (2) the total time in the air, (3) the range of the projectile, (4) the velocity of the projectile 2 s after firing.
- A daredevil drove his motorcycle up an incline at 30 degree angle with the horizontal and got air borne at the end of the incline at 20 m/s, 11 m above the ground. How far horizontally did he land with his motorcycle on the ground, on a safety net?A rocket is landing vertically downward from a point 2 miles east of an observer on the ground. What is the speed of the rocket when the angle of elevation of the observer's line of sight to the rocket is 50° and is decreasing 5° per second?A diver leaves a 3-mm board on a trajectory that takes her 2.8 mm above the board and then into the water 2.6 mm horizontally from the end of the board At what speed did she leave the board? At what angle did she leave the board?
- A fireworks show is choreographed to have two shells cross paths at a height of 154 feet and explode at an apex of 191 feet under normal weather conditions. If the shells have a launch angle θ = 56° above the horizontal, determine the common launch speed v0 for the shells, the separation distance d between the launch points A and B, and the time t from the launch at which the shells explode.A projectile is fired from a cliff 190 feet above the water at an inclination of 45 degree to the horizontal ,with muzzle velocity of 45 feet per second. The height h of the projectile above the water is given by h(x)=-32x^2/((45)^2) +x+190 Where x is the horizontal distance of the projectile from the face of the cliff. (A) At what distance from the face of the cliff is the height of the projectile a maximum?A ball is tossed horizontally from the highest point of a 75 m building and lands 150 m from the base of the building. Ignore air resistance, and use a coordinate system whose origin is at the highest point of the building, with positive y upwards and positive x in the direction of the throw. How long is the ball in the air for, in seconds?