Kinematics in Two Dimensions

In summary, the conversation discussed a quarterback's claim of being able to throw a football 171 meters at a low angle of 26.2 ° above the horizontal. To evaluate this claim, the speed of the throw must be determined. The relevant equations for projectile motion were mentioned, but the difficulty lies in not having enough information to solve the problem. However, it was suggested that the range of the projectile can be calculated using the formula R = v^2*sin(2θ) /g, and by plugging in the given values, the speed can be determined. The conversation ends with a request for an explanation of how this formula was derived.
  • #1
Phoenix838
2
0

Homework Statement



A quarterback claims that he can throw the football a horizontal distance of 171 m. Furthermore, he claims that he can do this by launching the ball at the relatively low angle of 26.2 ° above the horizontal. To evaluate this claim, determine the speed with which this quarterback must throw the ball. Assume that the ball is launched and caught at the same vertical level and that air resistance can be ignored. For comparison a baseball pitcher who can accurately throw a fastball at 45 m/s (100 mph) would be considered exceptional.

Homework Equations



vx = v0x + axt
vy = v0y + ayt
x = 1/2(v0x + vx)t
y = 1/2(v0y + vy)t
x=v0xt + 1/2axt2
y=v0yt + 1/2ayt2
vx2 = v0x2 + 2axx
vy2 = v0y2 + 2ayy



The Attempt at a Solution



The difficulty that I'm having is it seems like I don't have enough information to solve the problem. I've got the horizontal distance (x) as 171 meters, the horizontal acceleration (ax) as 0 m/s2, the vertical distance (y) as 0 meters and the vertical acceleration (ay) as -9.80 m/s2.

I know all I need is one more variable in order to solve this problem, but I just can't seem to figure out what I'm missing given the information I've got.
 
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  • #2
Using the relevant equations, you can show that the range of the projectile is given by
R = v^2*sin(2θ) /g. Using this formula find v.
 
  • #3
rl.bhat said:
Using the relevant equations, you can show that the range of the projectile is given by
R = v^2*sin(2θ) /g. Using this formula find v.

Would you mind explaining how you came up with that formula?
 

1. What is kinematics in two dimensions?

Kinematics in two dimensions is the branch of physics that studies the motion of objects in two-dimensional space. It involves analyzing the position, velocity, and acceleration of an object as it moves along a flat surface, such as a table or a graph.

2. What are the key concepts in kinematics in two dimensions?

The key concepts in kinematics in two dimensions include displacement, velocity, acceleration, and time. Displacement refers to the change in an object's position, velocity is the rate of change of displacement, acceleration is the rate of change of velocity, and time is the duration of the motion.

3. What are the differences between scalar and vector quantities in kinematics?

Scalar quantities in kinematics only have magnitude, such as distance or speed, while vector quantities have both magnitude and direction, such as displacement or velocity. This means that scalar quantities can be represented by a single number, while vector quantities require both a number and a direction.

4. How is the motion of an object represented in kinematics in two dimensions?

The motion of an object in kinematics in two dimensions can be represented by a position-time graph, a velocity-time graph, or an acceleration-time graph. These graphs show how the object's position, velocity, and acceleration change over time.

5. What are some real-life applications of kinematics in two dimensions?

Kinematics in two dimensions has many real-life applications, such as in sports, navigation, and engineering. For example, understanding the motion of a baseball in flight can help a pitcher improve their throw, and analyzing the motion of a car can help engineers design safer and more efficient vehicles.

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