Can someone please help me with the last 4 questions in this paragraph?
Suppose that Tiger hit a golf ball with an initial velocity of 150 ft/sec at an angle of elevation of 30°. Write the parametric equations to represent the flight of the ball. How long is the golf ball in the air? Determine the distance the ball traveled. When is the ball at its maximum height? What is the maximum height?
(a)
If you got the equations, answering the last 4 questions should be no sweat.
(b)
the ball is in the air while y(t)>0.That is, solve for t when y=0.
(c)
Knowing how long it took to hit, plug that into x(t).
(d)
y(t) is just a parabola. As usual, the vertex (where the ball had maximum height) is at t = -b/2a.
(e) use that t to get y(t), the maximum height.
Sure, I'd be happy to help you with the last four questions!
1. How to write parametric equations to represent the flight of the ball:
To represent the flight of the ball with parametric equations, we need to break down the motion into horizontal (x-direction) and vertical (y-direction) components. Let's assume the ball was launched from the origin (0,0).
The horizontal component, x(t), can be represented by the equation:
x(t) = V0*cos(θ)*t
where V0 is the initial velocity (150 ft/sec) and θ is the angle of elevation (30°).
The vertical component, y(t), can be represented by the equation:
y(t) = V0*sin(θ)*t - (1/2)*g*t^2
where g is the acceleration due to gravity, approximately 32.2 ft/sec^2.
So, the parametric equations to represent the flight of the ball are:
x(t) = 150*cos(30°)*t
y(t) = 150*sin(30°)*t - (1/2)*32.2*t^2
2. How to find the duration of the ball's flight:
The duration of the ball's flight can be determined by finding the time when the ball hits the ground. At that moment, y(t) = 0. We can solve this equation to find the time.
0 = 150*sin(30°)*t - (1/2)*32.2*t^2
By solving this quadratic equation, you can find the time t when the ball hits the ground, which represents the duration of its flight.
3. How to calculate the distance traveled by the ball:
The distance traveled by the ball can be determined by calculating the horizontal displacement, which is the value of x(t) at the moment the ball hits the ground. Using the time t found in the previous step, substitute it into the x(t) equation to get the distance traveled.
4. How to find the time at which the ball reaches its maximum height:
The ball reaches its maximum height at the highest point of its trajectory, where the vertical velocity is 0. To find this time, we can find the time t when the vertical velocity, vy(t), is equal to 0. The equation for vy(t) is the derivative of y(t) with respect to t. So, find vy(t) and solve it for t to determine the time at which the ball reaches its maximum height.
5. How to calculate the maximum height reached by the ball:
To calculate the maximum height, substitute the time t found in the previous step into the y(t) equation. This will give you the value of y at the highest point, which represents the maximum height reached by the ball.
I hope this helps you understand how to answer the last four questions in the paragraph!