Projectile Fired Over a Hill: Find H, R, Angle & t_g

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In summary, the conversation discusses solving for various values related to a projectile fired at an angle with a given initial velocity. This includes finding the highest point in the trajectory, expressing it in terms of gravitational acceleration, initial velocity, and angle, as well as determining the range of the projectile and the angle at which it should be fired. Additionally, the initial speed and flight time of the projectile are also requested, with the suggestion to use kinematic equations to solve for these values. It is also mentioned that the X and Y components of velocity are independent from each other.
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markiii
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A projectile is fired with speed v_0 at an angle
Find the highest point in the trajectory,H .
Express the highest point in terms of the magnitude of the acceleration due to gravity g, the initial velocity v_0, and the angle .
What is the range of the projectile,R ?
Express the range in terms of v_0,angle , and g.
Find the angle above the horizontal at which the projectile should be fired.
What is the initial speed?
Find t_g , the flight time of the projectile
 
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  • #2
Use the kinematic equations to solve for all of the requested values.
 
  • #3
Show some of ur own workings first. Like what Saketh have suggested. use the kinematics eqns to solve ur problem. These qns are quite straightforward.
 
  • #4
markiii said:
A projectile is fired with speed v_0 at an angle
Find the highest point in the trajectory,H .
Express the highest point in terms of the magnitude of the acceleration due to gravity g, the initial velocity v_0, and the angle .
What is the range of the projectile,R ?
Express the range in terms of v_0,angle , and g.
Find the angle above the horizontal at which the projectile should be fired.
What is the initial speed?
Find t_g , the flight time of the projectile

Decompose the velocity as x and y components first.
the X and Y components are independent to each other
 

1. What is the formula for finding the height of a projectile fired over a hill?

The formula for finding the height (H) of a projectile fired over a hill is H = (v^2*sin^2(theta))/2g, where v is the initial velocity of the projectile, theta is the angle of elevation, and g is the acceleration due to gravity.

2. How do you find the horizontal range (R) of a projectile fired over a hill?

The formula for finding the horizontal range (R) of a projectile fired over a hill is R = (v^2*sin(2*theta))/g, where v is the initial velocity of the projectile, theta is the angle of elevation, and g is the acceleration due to gravity.

3. What is the significance of the angle of elevation in calculating the trajectory of a projectile fired over a hill?

The angle of elevation plays a crucial role in calculating the trajectory of a projectile fired over a hill. It determines the initial vertical and horizontal velocities of the projectile, which ultimately affect its height, range, and time of flight.

4. How do you calculate the time of flight (tg) of a projectile fired over a hill?

The formula for calculating the time of flight (tg) of a projectile fired over a hill is tg = 2v*sin(theta)/g, where v is the initial velocity of the projectile, theta is the angle of elevation, and g is the acceleration due to gravity.

5. Can the calculations for a projectile fired over a hill be applied to real-life scenarios?

Yes, the calculations for a projectile fired over a hill can be applied to real-life scenarios, such as a golf ball being hit over a hill or a cannonball being fired over a castle wall. However, it is important to note that these calculations make certain assumptions and may not be completely accurate in real-life situations due to factors such as air resistance and wind.

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