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A rock is thrown upward from level ground in such a way that the maximum height of its flight, ymax, is equal to its horizontal distance d it travels before landing. (a) At what angle theta is the rock thrown? (b) Would your answer to part (a) be different on a different planet? Why? Hint for part (a): Make a sketch. Write out separate equations for vertical and horizontal motion, introducing a time variable. Relate the two equations to solve for theta.

The amusement ride shown is initially travelling on a circular path in a horizontal plane about O with v = 5 ê ft/s and r = 30 ft. The length of the cable is then decreased by a constant rate of 2 ft/s. Determine the speed of the cart after 3 seconds.

%3D , unit for r The appropriate units consistent with the SI system are: unit for T (Select] ,and unit for v (Select] The expression for calculating the orbital period of an object undergoing uniform circular motion is given by: T = | Select)

An object thrown from a height of 2 m above the ground follows a parabolic path until the object falls to the ground. If the object reaches a maximum height of 7 m after travelling horizontal distance of 4 m, determine the horizontal distance between the object's final position and final position.

A rodeo horse is running around a corral at a speed of 300 ft/s. Let x(t) be the distance of the horse from the third barrel and y(t) his distance from the fourth. (see figure; note that the distance between barrels is 900 řt). At what rate is the horse's distance from the fourth barrel changing at the instant when he is 200 ft from the third? 2 1 3 4

The banded archerfish is a species of fish that lives in mangrove estuaries in Asia and Oceania. It has a unique and highly effective hunting strategy: it shoots an incredibly precise stream of water out of its mouth at almost ten meters per second, knocking insects and other small animals into the water from nearby branches! Pom Fbug (t) Ө = Our hero, a hungry archerfish, has spotted a big, delicious bug sitting on a branch a height ħ above the surface of the water. The archerfish can shoot its water jet at a speed of vo. The archerfish wants to knock the bug sideways off of the branch, so it decides to shoot so that its water jet is moving horizontally at the moment when it strikes the bug. The final goal of this problem is to find the horizontal distance, d, from the branch, and the angle above horizontal, 0, at which archerfish should shoot. d (a) What are the position and velocity of the water droplet as a function of time and the position and velocity of the bug as a function of…

On a planet very similar to Earth, but slightly denser, where acceleration due to gravity is 10 m/s2, a projectile is fire vertically from a height of 100 meters with an initial velocity of 40 m/s. Its position above the ground after t seconds is given by h(t) = 100 + 40t − 5t2 meters.find the velocity of the projectile as it hits the ground

How would  I begin to solve this problem? In Example 2.6, we considered a simple model for a rocket launched from the surface of the Earth. A better expression for a rocket's position measured from the center of the Earth is given by y(t) = (RE3/2 + 3*(g/2)1/2 REt)2/3 where RE is the radius of the Earth (6.38 ✕ 106 m) and g is the constant acceleration of an object in free fall near the Earth's surface (9.81 m/s2). (a) Derive expressions for vy(t) and ay(t). (Use the following as necessary: g, RE, and t. Do not substitute numerical values; use variables only.)

An object is launched at a velocity of 35 m/s in a direction making an angle of 53 degrees upward with the horizontal. What is the horizontal range of the object in m?