Projectile on horizontal surface

In summary, the conversation discusses a problem involving a particle projected at an angle A with a given speed and range. The attempt at a solution includes equations for the horizontal and vertical components of the particle's motion, as well as a math error that is eventually resolved. The final equation found is 9.6 = sin2A.
  • #1
Darth Frodo
212
1

Homework Statement



A particle is projected with a speed of 98 m s−1 at an angle A to the horizontal.
The range of the particle is 940·8 m. Find
(i) the two values of A

The Attempt at a Solution



U = 98cosAi + 98sinAj

i direction

s = ut
940.8 = 98cosAt

j direction

s = ut + (0.5)at[itex]^{2}[/itex]
0= 98sinAt - (0.5)gt[itex]^{2}[/itex]
98sinA = gt/2
t = 20sinA

i direction
940.8 = (20sinA)(98cosA)
94.8 = (2sinAcosA)g
94.8 / g = sin2A



And I end up with a math error. Help please.
 
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  • #2
Darth Frodo said:
940.8 = (20sinA)(98cosA)
94.8 = (2sinAcosA)g

Oops.
 
  • #3
Ooops, sadly it doesn't solve the problem.

94.08 = 2sinAcosA(9.8)
94.08 / 9.8 = sin2A
9.6 = sin2A

math error
 
  • #4
Darth Frodo said:
94.08 = 2sinAcosA(9.8)

This equation doesn't follow from 940.8 = (20)sinAcosA(98)
 
  • #5
AHHH! Stupid error! Thanks!
 

1. What is a projectile on a horizontal surface?

A projectile on a horizontal surface refers to an object that is launched or thrown with an initial velocity and follows a curved path due to the force of gravity, eventually landing on a flat surface.

2. What are the factors that affect the path of a projectile on a horizontal surface?

The path of a projectile on a horizontal surface is affected by its initial velocity, angle of launch, air resistance, and the force of gravity.

3. How do you calculate the range of a projectile on a horizontal surface?

The range of a projectile on a horizontal surface can be calculated using the equation R = (v2sin2θ)/g, where R is the range, v is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity.

4. What is the maximum height a projectile can reach on a horizontal surface?

The maximum height a projectile can reach on a horizontal surface is determined by the equation H = (v2sin2θ)/(2g), where H is the maximum height reached. This occurs when the projectile is launched at a 45-degree angle.

5. How does air resistance affect the motion of a projectile on a horizontal surface?

Air resistance, also known as drag, can affect the motion of a projectile on a horizontal surface by slowing it down and altering its trajectory. This is because air resistance is a force that acts in the opposite direction of the projectile's motion, causing it to lose speed and height.

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