
36. A math book is lobbed from a height of 4 feet above the ground at...
Consider a projectile launched at a height h feet above the ground and at an angle θ with the horizontal. If the initial velocity is v0 feet per second, the path of the projectile is modeled by the parametric equations x = t(v0 cos(θ)) and y = h + (v0 sin(θ))t − 16t2. The center field fence in a ballpark is 10 feet high and 400 feet from home plate. The ball is hit h = 2 feet above the...
A baseball is hit by the batter when the ball is 2.5 feet above the ground. The ball leaves the bat with a velocity of 85 miles per hour at an angle of 50° above the horizontal. a. What is the maximum height of the baseball? b. When does the baseball reached its maximum height? c. If the ball does not hit anything, how many seconds is the ball in the air? d. If the ball does not hit anything,...
A ball is kicked from flat ground with a velocity of 10 m/s at an angle of 40 degrees ccw from the horizontal. a. What are the horizontal and vertical components of the velocity just as the ball leaves the hand? b. What is the horizontal and vertical velocity of the ball when it reaches maximum height? c. At what time does the ball reach maximum vertical height? d. How far has the ball traveled vertically and horizontally at maximum...
A rocket is fired upward from some initial distance above the ground. Its height in feet, h,above the ground, t seconds after it is fired, is given by h= -16t^2+32t+3584. What is the rocket's maximum height? ___ ft How long does it take for the rocket to reach its maximum height? t= ___sec After it is fired, the rocket reaches the ground at t= ___ sec.
all is thrown upward and outward from a height of 6 feet. The height of the ball. f(x), in feet, can be modeled by f(x)0.8.x2 +3.2x +6, where x is the ball's horizontal distance in feet, from where it is thrown. 14 pts] a. What is the maximum height of the ball and how far from where it was thrown does it occur? How far does the ball travel horizontally before hitting ground. Round to the nearest tenth of a...
A ball is launched from ground level at 30 m/s at an angle of 35˚ above the horizontal. (a) Find the speed of the ball when it reaches the maximum height.
18) A ball is thrown across a playing field from a height of 5 ft above the ground at an angle of 45° to the horizontalat a speed of 20 ft/s. It can be deduced fromphysical principles thatthe path of the ball is modeled by the function f(x) = - 32 x +x+5 400 a. At what horizontal distance xis the ball 7 ft high? b. At what horizontal distance x does the ball hit the ground?
The quarterback of a football team releases a pass at a height of 5 feet above the playing field, and the football is caught by a receiver 25 yards directly downfield at a height of 3 feet. The pass iis released at an angle of 35° with the horizontal. (a) Find the speed of the football when it is released. (Round your answer to three decimal places.) 49 77 x ft/sec (b) Find the maximum height of the football. (Round...
A ball is shot from the ground into the air. At a height of 9.40 m, the velocity is observed to be v = (7.80 m/s) i + (6.40 m/s) j. What is the maximum height that the ball will rise? What will be the total horizontal distance traveled by the ball? What is the x-component of the final velocity of the ball? What is the y-component of the final velocity of the ball when it lands back on the...
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A ball is thrown upward from a height of 1000 feet above the ground, with an initial velocity of 80 feet per second. From physics it is known that the acceleration at time t is a(t) = -32 feet per second squared. Use antiderivatives to find s(t), the function giving the height of the ball at timet.