Physics: Motion problem

**qbkr21** · January 31st 2009, 01:01 PM

No Calculus allowed. I need some help. I'm really stuck...

Thank You.

**skeeter** · January 31st 2009, 01:31 PM

no calculus, huh?

since $\Delta y = 0$

$0 = v_{yo}t - \frac{1}{2}gt^2$

$0 = t\left(v_{yo} - \frac{1}{2}gt\right)$

$v_{yo} = \frac{1}{2}gt$

$t = \frac{2v_{yo}}{g} = \frac{2v_o\sin{\theta}}{g}$

$\Delta x = v_x \cdot t$

$\Delta x = v_o\cos{\theta} \cdot \frac{2v_o\sin{\theta}}{g}$

$\Delta x = \frac{v_o^2 \cdot 2\sin{\theta}\cos{\theta}}{g}$

$\Delta x = \frac{v_o^2 \sin(2\theta)}{g}$

max value for $\Delta x$ occurs when $\sin(2\theta) = 1$

$\Delta x_{max} = \frac{v_o^2}{g}$

min ball speed will occur when it is at the peak of its trajectory ... when $v_y = 0$ ... min speed would therefore be ... ?

max height occurs at $t = \frac{v_{yo}}{g}$

**qbkr21** · January 31st 2009, 01:55 PM

Originally Posted by skeeter

no calculus, huh?

since $\Delta y = 0$

$0 = v_{yo}t - \frac{1}{2}gt^2$

$0 = t\left(v_{yo} - \frac{1}{2}gt\right)$

$v_{yo} = \frac{1}{2}gt$

$t = \frac{2v_{yo}}{g} = \frac{2v_o\sin{\theta}}{g}$

$\Delta x = v_x \cdot t$

$\Delta x = v_o\cos{\theta} \cdot \frac{2v_o\sin{\theta}}{g}$

$\Delta x = \frac{v_o^2 \cdot 2\sin{\theta}\cos{\theta}}{g}$

$\Delta x = \frac{v_o^2 \sin(2\theta)}{g}$

max value for $\Delta x$ occurs when $\sin(2\theta) = 1$

$\Delta x_{max} = \frac{v_o^2}{g}$

min ball speed will occur when it is at the peak of its trajectory ... when $v_y = 0$ ... min speed would therefore be ... ?

max height occurs at $t = \frac{v_{yo}}{g}$

How did you figure all of these side details out like delta y = 0?

How do you determine which parts of the problem belong to X and which ones belong to y ?

For the last part can you at least show me the equations that I would use?

Thanks,
qbkr21

**skeeter** · January 31st 2009, 02:47 PM

How did you figure all of these side details out like delta y = 0?

if the projectile starts on the ground and ends on the ground, what is $\Delta y$ ?

How do you determine which parts of the problem belong to X and which ones belong to y ?

I don't understand the question ... what parts do you mean?

For the last part can you at least show me the equations that I would use?

I gave you the equation for time to the top of the projectile's trajectory ... you need to calculate $\Delta y$ for that time.

$\Delta y = v_{yo}t - \frac{1}{2}gt^2$

you could also ignore the time element and use this equation to calculate $\Delta y$ ...

$v_{yf}^2 = v_{yo}^2 - 2g(\Delta y)$

at the top of its trajectory, $v_{yf} = 0$

**qbkr21** · January 31st 2009, 03:49 PM

Question:

b) What is the minimum speed of the ball during this hole-in-one shot?

The book says the answer is 21.2 m/s

I set up my equation as follows...

(V_y)^2=(V_xy)^2-2g*delta(y)
0=V_xy)^2-1799.28
x^2=1799.28
x=42.4

***Where did I go wrong?

**skeeter** · January 31st 2009, 06:49 PM

at the top of its trajectory, the projectile's y-component of velocity is zero ... so, it only has an x-component of velocity which is constant since there is no acceleration in the x-direction.

$v_x = v_o\cos{\theta}$

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