The ball spins at 7.7 rev/s. In addition, the ball is through with a linear speed of 19 m/s at an angle of 55 degrees with respect to the ground. If the ball is caught at the same height at which it left the quarterback's hand, how many revolutions has the ball made in the air?
Thanks for your help
bobpursley earlier wrote this but I still do not know where all the letters stand for. Could someone help me solve it. Thanks bobpusrley for your help
The vertical speed of the ball is 19sin55.
hf=ho+viy*t- 1/2 g t^2
0=19sin55*t-4.9t^2
solve for time in air, t.
revolutions= 7.7*timeinair
final height= initial height+ velocity vertical initial*time minus 1/2 acceleartion due to gravity*time^2
but how do I know the final height, initial height, and velocity vertical initial
final height and initial height are the same, so they cancel out of BobPurley's equation. You don't have to know them.
The vertical initial velocity is 19 sin55. You calculate that.
Then solve for t as indicated by Bob
25
To solve this problem, we need to break it down into smaller steps. Let's go through the steps mentioned by bobpursley:
Step 1: Find the vertical speed of the ball.
The vertical speed can be found using the given linear speed and angle. The formula to find the vertical speed is:
Vertical speed = Linear speed * sin(angle)
Using the given values:
Vertical speed = 19 m/s * sin(55 degrees)
Vertical speed ≈ 15.4 m/s
Step 2: Use the kinematic equation to find the time in the air.
The height of the ball at any time during its flight can be calculated using the kinematic equation for vertical motion:
hf = ho + viy * t - 1/2 * g * t^2
Here, hf and ho are the final and initial heights respectively, viy is the vertical component of velocity, t is the time in the air, and g is the acceleration due to gravity.
Since the ball is caught at the same height it left the quarterback's hand, hf = ho, which means the equation becomes:
0 = viy * t - 1/2 * g * t^2
Plugging in the values:
0 = 15.4 m/s * t - 4.9 m/s^2 * t^2
This is a quadratic equation. By solving it, you can find the time of flight (t). Use the quadratic formula or any other method to find the time.
Step 3: Calculate the number of revolutions.
The number of revolutions can be found by multiplying the time in the air (t) by the given spin rate of the ball:
Revolutions = spin rate * time in air
Plugging in the values:
Revolutions = 7.7 rev/s * time in air
By substituting the value of t obtained in step 2, you can calculate the number of revolutions.