Exam 12: Section 3: Vector-Valued Functions

The quarterback of a football team releases a pass at a height of 8 feet above the playing field, and the football is caught by a receiver 38 yards directly downfield at a height of 4 feet. The pass is released at an angle of with the horizontal. Find the speed of the football when it is released. Round your answer to three decimal places.

The quarterback of a football team releases a pass at a height of 8 feet above the playing field, and the football is caught by a receiver 46 yards directly downfield at a height of 4 feet. The pass is released at an angle of with the horizontal. Find the time in seconds the receiver has to reach the proper position after the quarterback releases the football. Round your answer to one decimal place.

The position vector describes the path of an object moving in the xy-plane. Sketch a graph of the path and sketch the velocity and acceleration vectors at the point .

The position vector describes the path of an object moving in space. Find the acceleration of the object.

Determine the maximum height of a projectile fired at a height of 6 feet above the ground with an initial velocity of 700 feet per second and at an angle of above the horizontal. Use the model for projectile motion, assuming there is no air resistance. Round your answer to three decimal places.

Use the given acceleration function and initial conditions to find the position at time t = 1.

The position vector describes the path of an object moving in space. Find the velocity of the object.

A baseball, hit 9 feet above the ground, leaves the bat at an angle of and is caught by an outfielder 9 feet above the ground and 500 feet from home plate. What is the initial speed of the ball? Round your answer to two decimal places.

The position vector describes the path of an object moving in space. Find the speed of the object.

Determine the range of a projectile fired at a height of 5 feet above the ground with an initial velocity of 1000 feet per second and at an angle of above the horizontal. Use the model for projectile motion, assuming there is no air resistance. Round your answer to three decimal places.

Find the vector-valued function for the path of a projectile launched at a height of 20 feet above the ground with an initial velocity of 50 feet per second at an angle of 35 degrees above the horizontal. Use a graphing utility to graph the path of the projectile and confirm your selection. Let i be the unit vector in the horizontal direction and j the unit vector in the vertical direction.

Use the given acceleration function and initial conditions to find the position at time t = 1.

The position vector describes the path of an object moving in space. Find the speed of the object.

The quarterback of a football team releases a pass at a height of 6 feet above the playing field, and the football is caught by a receiver 76 yards directly downfield at a height of 2 feet. The pass is released at an angle of with the horizontal. Find the maximum height of the football. Round your answer to one decimal place.

A baseball, hit 5 feet above the ground, leaves the bat at an angle of and its caught by an outfielder 5 feet above the ground and 500 feet from home plate. How high does the ball rise? Round your answer to the nearest integer.

A baseball player at second base throws a ball 87 feet to the player at first base. The ball is thrown 5 feet above the ground with an initial velocity of 50 miles per hour and at an angle of above the horizontal. At which height does the player at first base catch the ball? Round your answer to three decimal places.

The position vector describes the path of an object moving in space. Find the velocity of the object.

Use the given acceleration function and initial conditions to find the position at time t = 3.