Finding Time of Flight/Maximum Height/Horizontal Range

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In summary, the conversation is about finding the time of flight, maximum height, and horizontal range given launch angle and initial velocity. The person attempted to use sine and cosine to find the horizontal range and maximum height for a launch angle of 9 degrees with an initial velocity of 25 m/s, but was told that it is not correct. They were advised to divide the initial velocity into x and y components and use kinematics to write out equations in terms of acceleration and velocity components. They were also reminded of the importance of being able to write equations without knowing all the variables involved.
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ZeshShawn
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Homework Statement


Find Time of Flight/Maximum height & horizontal range given Launch Angle and Initial Velocity.

Using Launch angles: 9, 27, 45, 63 & 81.
Initial Velocity: 25 m/s


Homework Equations





The Attempt at a Solution


I used sine/cosine to find the Horizontal Range & Maximum height.

For launch angle 9°:
Maximum Height: 25sin9 =
Horizontal Range: 25cos9 =

I don't know if It's correct, also, I do not know how to find the Time of flight.

Please help.

Thanks.
 
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  • #2
That would not be correct.
if the launch angle were 9deg, then 25sin(9) would be the y-component of the velocity.You need to divide the initial velocity into x and y components.
Since the launch angle varies, you just leave it as ##\theta##.

From there - use kinematics to write out the maximum height and range equations in terms of the acceleration (you know this) in each direction and the velocity components.
You'll have to include an extra time of flight (T) term which you eliminate to get the final relations.

It is an important discipline in physics to be able to write down equations without knowing what parts of them are.
 

1. How do you calculate the time of flight for a projectile?

The time of flight for a projectile can be calculated using the formula t = 2v*sin(theta)/g, where v is the initial velocity, theta is the angle of launch, and g is the acceleration due to gravity (9.8 m/s^2). This formula assumes no air resistance.

2. What is the maximum height reached by a projectile?

The maximum height reached by a projectile can be calculated using the formula h = (v^2*sin^2(theta))/2g, where v is the initial velocity, theta is the angle of launch, and g is the acceleration due to gravity (9.8 m/s^2). This formula also assumes no air resistance.

3. How do you determine the horizontal range of a projectile?

The horizontal range of a projectile can be calculated using the formula R = v^2*sin(2*theta)/g, where v is the initial velocity, theta is the angle of launch, and g is the acceleration due to gravity (9.8 m/s^2). This formula also assumes no air resistance.

4. Does air resistance affect the time of flight, maximum height, and horizontal range of a projectile?

Yes, air resistance can affect the time of flight, maximum height, and horizontal range of a projectile. The above formulas assume no air resistance, so if air resistance is present, these values will be slightly different. To account for air resistance, more complex equations and simulations are needed.

5. How does the angle of launch affect the time of flight, maximum height, and horizontal range of a projectile?

The angle of launch greatly affects the time of flight, maximum height, and horizontal range of a projectile. A higher angle will result in a longer time of flight and a higher maximum height, but a shorter horizontal range. Conversely, a lower angle will result in a shorter time of flight and a lower maximum height, but a longer horizontal range. The optimal angle for maximum distance is 45 degrees.

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