A horizontal projectile with mass of 19.0kg is launched from a height of 7.0m above ground level with a horizontal speed of 250.0m/s.
A)During projectile's flight, what forces are acting on it?
B)What are the sizes & directions of the forces?
C)Assuming ground below flight path remains level, what is the vetical speed of the projectile as it hits the ground?
D)What is the flight time of the projectile?
E)What was the horizontal distance traveled?
F)How much work is done on the projectile?
A) During the projectile's flight, there are three main forces acting on it:
1. Gravitational force: which pulls the projectile downward towards the ground.
2. Normal force: which is exerted by the ground and acts perpendicular to the ground surface to support the weight of the projectile.
3. Air resistance: which opposes the projectile's motion and depends on various factors such as speed, shape, and surface area.
B) The sizes and directions of the forces are as follows:
1. Gravitational force: The size of the gravitational force is determined by the mass of the projectile (19.0kg) and the acceleration due to gravity (approximately 9.8 m/s^2). The direction of the gravitational force is downward.
2. Normal force: The size of the normal force is equal and opposite to the gravitational force. It balances the force of gravity, so the net vertical force is zero. The direction of the normal force is upward.
3. Air resistance: The size and direction of air resistance depend on the specific circumstances of the projectile's motion, such as the shape and velocity. For simplicity, let's assume there is no air resistance, so its size and direction would be negligible.
C) Assuming there is no air resistance, the only vertical force acting on the projectile is the force of gravity. As the projectile falls freely, the vertical speed at impact will be equal to the initial vertical velocity. Given that the projectile was launched horizontally, the initial vertical velocity is zero. Therefore, the vertical speed of the projectile as it hits the ground is 0 m/s.
D) To find the flight time of the projectile, we can use the formula: time = distance / speed.
Since the projectile is launched horizontally, its vertical distance is zero. Therefore, we need to find the horizontal distance traveled.
E) To find the horizontal distance traveled, we can use the formula: distance = speed * time.
Given that the horizontal speed is 250.0 m/s and the time is unknown, we cannot directly calculate the horizontal distance traveled without knowing the flight duration (time).
To determine the answers to these questions, we need to apply the principles of projectile motion and consider the forces acting on the projectile.
A) During the projectile's flight, there are two main forces acting on it: gravitational force (weight) and air resistance (drag).
B) The gravitational force always acts downward and can be calculated using the equation:
Weight = mass x gravitational acceleration
Weight = 19.0 kg x 9.8 m/s^2 = 186.2 N
Therefore, the force due to gravity is 186.2 N and acts vertically downwards.
The force of air resistance can vary depending on the shape and speed of the projectile. In this case, we don't have specific information about the object's shape or the characteristics of the medium it's traveling through, so we cannot determine the exact magnitude and direction of the air resistance force.
C) Assuming no other forces are acting horizontally, the vertical speed of the projectile as it hits the ground can be determined using the equation:
Final velocity^2 = Initial velocity^2 + 2 x acceleration x distance
The acceleration is due to gravity and is equal to -9.8 m/s^2 (negative denotes downward direction), the initial velocity is 0 m/s (at its highest point), and the distance is the height from which the projectile was launched (7.0 m above ground level).
0^2 = 200^2 + 2 x -9.8 x 7.0
0 = 40000 - 1372
1372 = 40000
So, the vertical speed of the projectile as it hits the ground is approximately 1372 m/s downward.
D) The flight time of the projectile can be calculated using the equation:
Flight time = Distance / Horizontal speed
Since the projectile is launched horizontally, its horizontal speed remains constant throughout the trajectory. The distance traveled horizontally is not given in the question, so we need to calculate it in order to find the flight time.
E) To determine the horizontal distance traveled, we can use the equation:
Distance = Horizontal speed x Time
The horizontal speed is given as 250.0 m/s, and the flight time can be calculated from the vertical motion of the projectile as discussed in part D.
F) To determine the work done on the projectile, we need to know the distance traveled, the force applied, and the angle between the applied force and the direction of motion. Unfortunately, the question does not provide information about the force applied to the projectile. Without this information, it is not possible to calculate the work done on the projectile.
In conclusion, we can answer parts A and B regarding the forces acting on the projectile. However, parts C, D, E, and F require more specific information that is not provided in the question.