A football is kicked with a speed of 18 m/s at an angle of 65° to the horizontal.
How long is the football in the air? Neglect air resistance
Would I use the equation
y=y0 + voy t -1/2gt^2 ?
that is correct. All you care about is the height.
Yes, with voy = 18 sin65 = 16.31 m/s
Set y = yo and solve for t
gt/2 = voy
t = 2*voy/g
Yes, you can use that equation to find the time the football is in the air. In the given equation, "y" represents the vertical position of the football, "y0" is the initial vertical position, "voy" is the initial vertical velocity, "t" is the time, and "g" is the acceleration due to gravity.
To find the time the football is in the air, you need to set the final vertical position "y" equal to zero, since the football reaches the ground. Therefore, the equation becomes:
0 = y0 + voy t - (1/2)gt^2
Since the football is kicked from the ground, the initial vertical position "y0" is zero. So the equation simplifies to:
0 = voy t - (1/2)gt^2
Now, rearrange the equation:
(1/2)gt^2 = voy t
Divide both sides of the equation by "t" to get:
(1/2)gt = voy
Finally, solve for "t":
t = 2voy / g
Remember that "voy" is the initial vertical velocity, which can be calculated using trigonometry. Since the football is kicked at an angle of 65° to the horizontal, you can find the vertical component of the velocity, "voy", by multiplying the initial speed (18 m/s) by the sine of the angle (65°).
voy = 18 m/s * sin(65°)
Using a calculator, you can find the value of "voy" and substitute it into the equation to find the time "t" that the football is in the air.
Yes, you can use the equation y = y0 + voyt - 1/2gt^2 to solve this problem. In this equation, y represents the vertical position of the football, y0 is the initial vertical position, voy is the initial vertical velocity, g is the acceleration due to gravity (-9.8 m/s^2), and t is the time.
To determine how long the football is in the air, you need to find the time it takes for the football to reach the ground. The final vertical position y of the football at this time will be equal to zero, since the ball will be on the ground.
So, let's break down the equation:
y = y0 + voyt - 1/2gt^2
Since the ball is kicked from the ground, the initial vertical position y0 will be zero. Therefore, the equation simplifies to:
y = voyt - 1/2gt^2
Since the vertical position y is zero when the ball hits the ground, we can write:
0 = voyt - 1/2gt^2
Rearranging this equation, we get:
1/2gt^2 = voyt
Dividing both sides of the equation by t, we get:
1/2gt = voy
Now, we can solve for t by dividing both sides of the equation by 1/2g:
t = (voy)/(1/2g)
Plug in the values:
- Initial vertical velocity, voy = 18 m/s
- Acceleration due to gravity, g = -9.8 m/s^2
t = (18 m/s) / (1/2 * -9.8 m/s^2)
By simplifying the equation further, you can find the value of t, which represents the time the football is in the air.