a cannon is used to provide the initial launch of a 400,000 kg rocket at an angle of 40° from the horizontal. if the rocket leaves the barrel of the cannon 10 meters from the ground at a velocity of 800 m/s, what is the peak height (y value) reached of the rocket, how far has the rocket traveled (x value) and how long will it take to reach the peak height?

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

A swimmer who can consistently keep the same pace to cover 50 meters in 6.8 seconds sets out to swim across a river. The current in the river moves at 3.2 meters per second as the swimmer keeps a constant pace trying to get directly across (at a right angle to the current).  What is the actual speed of the swimmer compared to land? (Your answer should be in meters per second. Remember to calculate a speed first, then add vectors using Pythagorean Theorem)

A golf ball is hit upward, with an initial velocity of 47 meters per second, at an angle of 25° with respect to the horizontal. The ball is hit from a height of 8 meters above the ground.   The horizontal distance x from the starting point and the height y above the ground of the ball t seconds after it is hit are given by the parametric equations below.   x=(v0cosθ)t y=−4.9t^2+(v0sinθ)t+h Here v0 is the initial velocity, θ is the initial angle with respect to the horizontal, and h is the initial height.   Use the equations to answer the following questions.   (a)How long is the ball in the air before it first touches the ground?Do not round any intermediate computations. Round your answer to the nearest hundredth. _____ seconds (b)What is the horizontal distance the ball travels before it first touches the ground?Round your answer to the nearest whole number. _____ meters

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

In a naval battle, a cruiser is attempting to fire on a frigate. The cruiser is a distance d₁ = 2,050 m to the east of the peak of a mountain on an island, as shown in the figure below. The frigate is attempting to evade cannon shells fired from the cruiser by hiding on the west side of the island. The initial speed of the shells that the cruiser fires is v₁ = 245 m/s. The peak of the mountain is h = 1,690 m above sea level, and the western shore of the island is a horizontal distance d₂ = 270 m from the peak. What are the distances (in m), as measured from the western shore of the island, at which the frigate will be safe from fire from the cruiser? (Note the figure is not to scale. You may assume that the height and width of the frigate are small compared to d₁ and h.) less than Need Help? Read It 0₁ Ja₂ m, or more than d₁ m

A ball is thrown horizontally from the top of a 61.5-m building and lands 113.8 m from the base of the building. Ignore air resistance. (Assume the ball is thrown in the +x direction and upward to be in the +y direction.) (a) How long is the ball in the air? (b) What must have been the initial horizontal component of the velocity? (Indicate the direction with the sign of your answer.) m/s (c) What is the vertical component of the velocity just before the ball hits the ground? (Indicate the direction with the sign of your answer.) m/s (d) What is the velocity (including both the horizontal and vertical components) of the ball just before it hits the ground? magnitude m/s direction ° counterclockwise from the +x-axis

A descent vehicle landing on the moon has a vertical velocity toward the surface of the moon of 29 m/s. At the same time , it has a horizontal velocity of 52.9m/s.At what speed does the vehicle move along its descent path?answer in m/sAt what angle with the vertical it its path? answer in degrees

I am having trouble trying to figure out the exact equation to set this up for.   A projectile launched with a speed of 34.7 m/s has a range of 122 m.  What was the projectile’s maximum height?

On a day when the wind is blowing toward the south at 5 m/s , a runner logs west at 1.6 m/s.what is the magnitude of velocity of the air relative to the runnerCalculate answer to one decimal.