Solving Projectile Problem: Initial Velocity from Cliff

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In summary, a cannon is fired at a 30 degree angle from a cliff 20m above a flat river bottom. The initial velocity of the projectile can be found by using the equation Vi cos 30t = 40, where t represents the time of flight. Another equation can be used to solve for the vertical part of the flight.
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Homework Statement



A cannon is fired at an angle of 30 degrees above the horizontal from a cliff that is 20m above a flat river bottom. What is the initial speed of the projectile if it is found to land 40m from the base of the cliff?



Homework Equations


g = 9.8ms^-2
Vi = initial velocity

The Attempt at a Solution


I know that Vi cos 30t = 40, but does the "t" represent the time taken for the entire projectile motion, or just the upper symmetrical parabolic trajectory? I'm stuck at Vi cos 30t = 40 because what I did after simply didn't make any sense at all.

I've been stuck on this question for days on end, please help me with it! Thanks! :D
 
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  • #2
The [itex]t[/itex] represents the entire time of flight, from your equation you can actually solve for it. Now how about a second equation for the vertical part of the flight?
 

1. What is a projectile problem?

A projectile problem is a type of physics problem that involves calculating the motion of an object that is launched into the air and follows a curved path due to the force of gravity. This type of problem typically involves finding the initial velocity, time of flight, maximum height, and range of the projectile.

2. How do you solve for the initial velocity in a projectile problem from a cliff?

To solve for the initial velocity in a projectile problem from a cliff, you can use the formula v0 = √(2gh), where v0 is the initial velocity, g is the acceleration due to gravity (9.8 m/s2), and h is the height of the cliff. This formula assumes that the projectile is launched horizontally from the top of the cliff.

3. What is the difference between initial velocity and final velocity in a projectile problem?

Initial velocity is the velocity of the object at the beginning of its motion, while final velocity is the velocity of the object at the end of its motion. In a projectile problem, the initial velocity is typically the velocity at which the object is launched, while the final velocity is the velocity at which the object hits the ground or another surface.

4. Can you solve for the initial velocity without knowing the height of the cliff?

No, you cannot solve for the initial velocity without knowing the height of the cliff. The initial velocity is a crucial component in calculating the trajectory of a projectile, and without knowing the height of the cliff, you cannot accurately determine the initial velocity.

5. What are some real-life applications of solving projectile problems?

Solving projectile problems has many real-life applications, such as calculating the trajectory of a rocket or missile, determining the optimal angle and speed for a shot in sports like basketball or golf, and predicting the motion of objects in freefall, such as bungee jumpers or skydivers.

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