A golfer hits a golf ball with an initial velocity of 100 miles per hour.The range R of the ball as a function of the angle θ   to the horizontal is given by where R ( θ)  =672sin(2θ) where R is measured in feet. (a) At what angle θ should the ball be hit if the golfer wants the ball to travel 450 feet (150 yards)? (b) At what angle  θshould the ball be hit if the golfer wants the ball to travel 540 feet (180 yards)? (c) At what angle θ   should the ball be hit if the golfer wants the ball to travel at least 480 feet (160 yards)? (d) Can the golfer hit the ball 720 feet (240 yards)?

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Q: Use the model for projectile motion, assuming there is no air resistance. Determine the maximum…

A: Please refer the attached image for complete solution.

Q: 3. A plane travelling at an altitude of 20,000 feet passes directly overhead at time t = 0. One…

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Q: The grade resistance F of a car traveling up or down a hill is modeled by the equation F = W sin θ,…

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Q: 2. A boy is flying a kite at a height of 50 meters. The kite is moving horizontally away from the…

A: Let's find.

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Q: se the model for projectile motion, assuming there is no air resistance and g = 32 feet per second…

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Q: 5. A ball is thrown following a projectile motion. It is known that the horizontal distance (range)…

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A:

Q: 4) Consider f(x) = 4 sin x, part of which is shown. The point A has coordinates (5,4) and the point…

A:

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A:

Q: 6) Calculating the Time of a Trip From a parking lot, you want to walk to a house on the beach. The…

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Q: A ball is thrown following a projectile motion. It is known that the horizontal distance (range) the…

A: We will find the answers to both parts as following.

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Q: The derivative of the trigonometric function y = x csc 3x is A. -csc 3x ( 1 + 3 cot 3x) B. csc 3x (1…

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Q: 2. у 3 sin x, у3D сos x, 0 <x< T/2

A:

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Q: A 22-centimeter pendulum moves according to the equation 0 = 0.21 cos(9t), where 0 is the angular…

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Q: A boat leaves a port traveling due east at 12 mi/hr. At the same​ time, another boat leaves the…

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Q: On the graph of f(x) = 2 sin(27x), points P and Q are at consecutive lowest and highest points with…

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Q: A dart is thrown upward with an initial velocity of 64 ft/s at an angle of elevation of 56°.…

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Q: A straight street of fixed width a metres on the horizontal ground is bounded on its parallel sides…

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Q: The curves 1(t) =(- 4t, tº, 4t“) and 2(t) = (sin(-t), sin(3t), t – T) intersect at the | origin.…

A:

Q: a) Consider the ODE describing the motion of a pendulum in presence of friction. Let 0 indicate the…

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Q: A dart is thrown upward with an initial velocity of 67 ft/s at an angle of elevation of 59°.…

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Q: angular velocity o (in radis) of a pendulum is -0.50 sin 2.01. Find the angular displacement 0 as a…

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Q: A baseball is hit when it is 3 ft above the ground. It leaves the bat with initial velocity of 181…

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Q: 2. a. A predator is flying at a constant speed along with a constant height of 150 m that will take…

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Q: C. Find the value of the indicated circular function for angle 0 whose terminal side passes through…

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Q: A boat leaves a port traveling due east at 12 mi/hr and at the same time another boat leaves…

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Q: The range R of a projectile is given as attached, where v0 is the initial velocity in feet per…

A:

Q: For a person at rest, the velocity v (in liters per second) of airflow during a respiratory cycle…

A: We will solve the following.

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Q: (b) Consider the triangle formed by the side of the house, ladder, and the ground. Find the rate at…

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Q: A projectile is launched at ground level with an initial speed of 54.0 m/s at an angle of 35.0°…

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Q: The curves f(x) = x² – 3x − 4 and g(x) = 3x - 9 intersect at the point (1,-6). Find the acute angle…

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Q: An airplane is flying at a constant speed at an altitude of 10, 000 ft on a line that will take it…

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A:

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Q: An object is oscillating at the end of a spring. Its position, in centimeters, relative to a fixed…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.