Solve Golf's Ocean Dilemma: Projectile Motion Help for a 20 Degree Drive

In summary, a golfer on a hill 4.0m above sea level hits a drive at an angle of 20 degrees that unfortunately slices to the right and goes into the ocean. The ball lands in the water 5.0 seconds after it was hit. Using the equation y = xtantheta - [gx^2/(2v^2cos^2theta)], where x is the horizontal distance covered and y is the vertical distance, we can determine the initial velocity of the ball. The golfer must also keep in mind that t = 2vsintheta/g, and that the ball travels in 2D motion. By using Pythagoras's theorem, the initial velocity can be calculated by combining the
  • #1
avb203796
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A golfer on a hill 4.0m above sea level hits a drive at an angle of 20 degrees, but unfortunately slices it to the right so that it goes into the ocean! If the ball lands in the briny 5.0 seconds after it was hit, what is the initial velocity of the ball? What height (above the cliff) did the ball reach before falling downward into the water? How far from the tee did it travel? How much later will he hear the splash of the ball? Assume sound travels at 343 m/s.
 
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  • #2
I am not even really sur ehow to get started with this problem!
 
  • #3
There is an equation like
y = xtantheta - [gx^2/(2v^2cos^2theta)] where x is horizontal distance covered andy is vertical distance. Use this and report if you still have problem. Also try deriving the above formula.
you must also be knowing that t = 2vsintheta/g
 
  • #4
Where did the equation involving the tangent come from? I do not remember my instructor going over any equations with a tangent in them.
 
  • #5
First find t fromthe horixontal equation x = vcostheta*t.
then substitute t in the equation y = vsintheta*t - 1/2g*t^2
 
  • #6
Juz letta me give u a little push in starting this qn..
It may seem like a 3D motion qn but it is actually juz 2D..

For the 1st part, u noe that the ball touches the water 5s after the golfer hits the ball.. u oso noe that the height (oso known as the displacement) above the water where the golfer hits is 4m.. u oso noe that the vertical acceleration for bodies in 2D motion is only gravity ( 9.81m/s^2) and what u wan now is the initial velocity.. note: <---this is vertical.. u still nid to get use pythagoras theorm on both the horizontal and vertical velocities to get the initial velocity..

I hope this gets u start off.. the rest shld be quite easy..
 

What is projectile motion?

Projectile motion is the motion of an object that is launched or thrown into the air and then moves under the force of gravity. It follows a curved path known as a parabola.

What are the key factors that affect projectile motion?

The key factors that affect projectile motion are initial velocity, launch angle, and the force of gravity. Other factors such as air resistance and the rotation of the Earth may also have small effects.

How can I calculate the horizontal and vertical components of a projectile's motion?

The horizontal and vertical components of a projectile's motion can be calculated using trigonometric functions. The horizontal component is equal to the initial velocity multiplied by the cosine of the launch angle, while the vertical component is equal to the initial velocity multiplied by the sine of the launch angle.

What is the formula for calculating the maximum height of a projectile?

The formula for calculating the maximum height of a projectile is h = (v02 * sin2θ) / 2g, where h is the maximum height, v0 is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity.

What is the range of a projectile and how can it be calculated?

The range of a projectile is the horizontal distance it travels before hitting the ground. It can be calculated using the formula R = (v02 * sin2θ) / g, where R is the range, v0 is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity.

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