A golfer hits a ball off a tee from an elevated platform 13m above the ground. if the golf ball leaves the tee at 85 m/s @ 15 degrees, find the flight time, the maximum height above the ground and the horizontal displacement of the golf ball.
Vo = 85m/s[15o]
Xo = 85*cos15 = 82.1 m/s.
Yo = 85*sin15 = 22 m/s.
Y = Yo + g8*Tr = 0 @ max ht.
22 - 9.8Tr = 0
9.8Tr = 22
Tr = 2.24 s. = Rise time.
0.5g*Tf^2 = h max = 37.7 m.
4.9Tf^2 = 37.7
Tf^2 = 7.69
Tf = 2.77 s. = Fall time.
T = Tr + Tf = 2.24 + 2.77 = 5 s. =
Flight time.
h max = ho + (Y^2-Yo^2)/2g
= 13 + (0-22^2)/-19.6 = 37.7 m.
Dx = Xo*T = 82.1m/s * 5s = 412 m.
To find the flight time, maximum height, and horizontal displacement of the golf ball, we can use the kinematic equations of motion.
1. Flight Time:
The flight time can be calculated using the vertical motion of the golf ball. The equation we can use is:
`y = y0 + v0y * t - 0.5 * g * t^2`
where:
y = final vertical position (in this case, 0, since the ball lands on the ground)
y0 = initial vertical position (13m)
v0y = vertical component of initial velocity (v0 * sin(theta))
g = acceleration due to gravity (9.8 m/s^2)
t = flight time
Plugging in the values:
0 = 13 + (85 * sin(15)) * t - 0.5 * 9.8 * t^2
We can solve this quadratic equation to find the flight time.
2. Maximum Height:
To find the maximum height, we can use the equation:
vfy = v0y - g * t
where:
vfy = final vertical velocity (0 m/s at maximum height)
v0y = vertical component of initial velocity (v0 * sin(theta))
g = acceleration due to gravity (9.8 m/s^2)
t = flight time
Solving for t in terms of v0y:
0 = v0y - 9.8 * t
t = v0y / 9.8
Substituting the value of t into the equation for height:
y = y0 + v0y * (v0y / 9.8) - 0.5 * 9.8 * (v0y / 9.8)^2
Simplifying this equation will give us the maximum height.
3. Horizontal Displacement:
The horizontal displacement can be calculated using the equation:
x = v0x * t
where:
x = horizontal displacement
v0x = horizontal component of initial velocity (v0 * cos(theta))
t = flight time
Plugging in the values, we can find the horizontal displacement.
Now, let's solve these equations step by step to find the flight time, maximum height, and horizontal displacement.