Physics 11 vector question ?

In summary, using the given equations and known initial velocity of 30 m/s, the widest river that a stone can be thrown across and end at the same vertical height is determined by finding the maximum distance or range. This is done by deriving an expression for the total distance, using the given equations and trigonometric identities, and solving for the angle of launch that produces the maximum range. The calculated time to reach the maximum range is then doubled to determine the total time of flight.
  • #1
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Homework Statement



A stone is thrown at 30 m/s. what is the widest river it can be thrown across? (the stones ends at the same vertical height from where it was thrown)

Homework Equations



x=vxot
y=vyot + 0.5gt2

The Attempt at a Solution


i know i need to find t first. using the second equation i got t as 5.2s. when i multiplied 5.2s by vxo (30m/s) i got 156.3 m but the answer should be 92m. wat did i do wrong?
 
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  • #2
You can't just use the V as Vx.

Vo is constrained to be 30 m/s.

I rather think they want you to derive the Range Equation and determine where range reaches its maximum.

Using your equations then, and

Vox = Vo*Cosθ

and

Voy = Vo*Sinθ

derive an expression for X, total distance, and then determine at what angle of launch you get the maximum.

Along the way you might find this useful ... 2*Cosθ*Sinθ = sin(2θ)
 
  • #3
well when i used x=vxot
i put in (30cos45)(5.2s) but i got 82m instead of 92 m
 
  • #4
roxxyroxx said:
well when i used x=vxot
i put in (30cos45)(5.2s) but i got 82m instead of 92 m

You maybe want to recalculate.

I get a different time which is less and the answer given - after rounding.
 
  • #5
how did u get ur time?
i can't seem to get any other answer than what i got..
 
  • #6
v = g*t

t = v/g

That's time to max. Double it to come back down.

v = 30*sin45 = 30*√2/2

30*√2/2*2/g = 30*√2/g = ... ?
 
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1. What are vectors in physics?

Vectors in physics are quantities that have both magnitude (size) and direction. They are represented by arrows, where the length of the arrow corresponds to the magnitude of the vector, and the direction of the arrow indicates the direction in which the vector is pointing.

2. How are vectors used in physics?

Vectors are used in many areas of physics, such as mechanics, electromagnetism, and thermodynamics. They are used to describe and analyze the motion of objects, forces acting on objects, and other physical quantities.

3. What is the difference between a scalar and a vector?

A scalar is a quantity that has only magnitude, whereas a vector has both magnitude and direction. Examples of scalars include temperature, time, and speed, while examples of vectors include displacement, velocity, and force.

4. How do you add and subtract vectors?

To add or subtract vectors, you can use the graphical method or the component method. In the graphical method, you draw the vectors to scale and use the parallelogram rule or the head-to-tail method to find the resultant vector. In the component method, you break the vectors down into their x and y components and then add or subtract the components separately.

5. Can vectors be multiplied?

Yes, vectors can be multiplied in two ways: scalar multiplication and vector multiplication. Scalar multiplication involves multiplying a vector by a scalar (a number), which changes the magnitude of the vector. Vector multiplication, also known as the dot product or cross product, involves multiplying two vectors together to produce a scalar or vector result, respectively.

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