How High Does a Golf Ball Go When Driven at 24.5 Degrees?

In summary, projectile motion is the curved path of an object in the air due to the force of gravity. Factors such as initial velocity, angle of launch, air resistance, and gravity affect this motion. The range of a projectile can be calculated using the equation R = (v^2 * sin(2θ)) / g. The horizontal and vertical components of this motion are independent and are affected differently by factors such as air resistance. The mass of a projectile does not affect its motion, as long as it remains constant, due to the cancellation of the force of gravity in the equation for projectile motion.
  • #1
richardjoe05
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A golfer drives a golf ball 310.24 m down the fairway. If the ball is launched at an angle of 24.5 o to the horizontal, what is the maximum height attained by the ball during its flight?


H=1/2gt^2
 
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  • #2
The maximum height attained is given by [tex] H = \frac{u^2 \sin^2 \theta}{2 g} [/tex] where u is the magnitude of the initial velocity provided and θ the angle with the horizontal.

The range of the projectile is [tex] R = \frac{u^2 \sin 2 \theta}{g} [/tex] which is given to be 310.24 m.

Thus we have [tex] H = \frac{R}{4} \tan \theta [/tex]
 

FAQ: How High Does a Golf Ball Go When Driven at 24.5 Degrees?

What is projectile motion?

Projectile motion is the motion of an object that is launched into the air and is subject to the force of gravity. This results in a curved path known as a parabola.

What factors affect projectile motion?

The factors that affect projectile motion include the initial velocity, angle of launch, air resistance, and the force of gravity.

How is the range of a projectile calculated?

The range of a projectile is calculated by using the equation R = (v^2 * sin(2θ)) / 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.

What is the difference between horizontal and vertical components of projectile motion?

The horizontal component of projectile motion refers to the motion along the x-axis, while the vertical component refers to the motion along the y-axis. These components are independent of each other and are affected differently by factors such as air resistance.

How does the mass of a projectile affect its motion?

The mass of a projectile does not affect its motion, as long as the mass is constant. According to Newton's Second Law, the acceleration of an object is directly proportional to the net force acting on it, and inversely proportional to its mass. Since the force of gravity is proportional to mass, it cancels out in the equation for projectile motion, making mass irrelevant.

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