How Far Will a Thrown Rock Travel and Will It Clear a Fence?

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In summary, the problem is to determine the distance a rock will travel if thrown with a horizontal velocity of 90ft/sec and a vertical velocity of 47 ft/sec from a point 3 ft above the ground, assuming there are no obstructions. Using parametric equations, the distance can be calculated using the equations x(t) = 90t and y(t) = -16t^2 + 47t + 3. Using physics, the final velocity vector of the rock can be found by adding the horizontal and vertical velocities, and then solving for the distance using the equation v^2 = v0^2 + 2ax. Ultimately, the distance is found to be 270 ft.
  • #1
Pi Face
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If a rock is thrown from a point 3 ft above the ground with a horizontal velocity of 90ft/sec and a vertical velocity of 47 ft/sec, how far away will it land if nothing is obstructing its path? If there is a 7'9" fence in front of you, will the rock sail over the fence?

Actually, this is a problem in my calc book. I'm supposed to solve it using parametric equations but I figured its still physics...

Using parametrics: the
x(t)=x0+h0t
x(t)=90t

y(t)=(-1/2)gt2+v0t+yo
y(t)=-16t2+47t+3

Using physics:
Not sure which equation to use. I'm a little confused. I started by adding the velocity vectors, and got 101.5 ft/s in an upwards diagonal direction
I used v2=v02+2ax
v=0, v0=101.5, solved for x and got 525.625.
answer should be 270. no idea what to do...

I'd prefer to work with the parametric method but any help is welcome...Thanks
 
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  • #2
y(t)=-16t^2+47t+3
Since the rock lands on the ground, take y(t) = 0. Solve for t.
 
  • #3
ah thanks. got it =)
 

FAQ: How Far Will a Thrown Rock Travel and Will It Clear a Fence?

What is parametrics in physics?

Parametrics in physics refers to the use of mathematical equations to describe and analyze the motion of objects. It involves using variables such as time, position, velocity, and acceleration to study the behavior of objects in motion.

How is parametrics different from kinematics?

Parametrics and kinematics are both branches of physics that deal with the study of motion. However, parametrics specifically focuses on using mathematical equations, while kinematics also includes the concepts of displacement, velocity, and acceleration without the use of equations.

What are some common applications of parametrics in physics?

Parametrics is commonly used in physics to analyze the motion of objects such as projectiles, pendulums, and simple harmonic oscillators. It is also used in fields such as engineering and robotics to design and control the motion of machines and structures.

How is parametrics used in real-world situations?

Parametrics is used in real-world situations to predict and understand the behavior of objects in motion. For example, parametric equations can be used to calculate the trajectory of a projectile, which is useful in fields such as ballistics and sports.

What mathematical skills are needed for understanding parametrics in physics?

A strong foundation in algebra and trigonometry is essential for understanding parametric equations in physics. It is also helpful to have a good grasp of calculus, as parametrics involves using derivatives and integrals to analyze the motion of objects.

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