Projectile Problem With Athlete

[krypto]

Projectile Problem With Athelete

This is the question:
An athlete executing a long jump leaves the ground at a 35° angle and travels 5.80 m.
a) What was the takeoff speed?
b) If this speed were increased by just 5.0 percent, how much longer would the jump be?

ive worked out the initial velocity = speed x sin 35 (is that rite)
i know it has somethin to do with the angle and sin but I am not sure how to put it onto an equation :S i keep getting 3.32 but its not rite :(
wat am i doing wrong?

 

[sevens]

Velocity as a vector or as its components?

well from what you state in the problem you know that
X inital is 0
X final is 5.8 m and
V final is 0.
a is the acceleration of gravity

if you just want to find the take off velocity you would use

$$(Vfinal)^2 = (Vinitial)^2 + 2a(Xfinal - Xinitial)$$

this gives you velocity as a vector if you want to break it down into x and y components then you would do

$$(Vinitial)*sin(theta)$$
for the y dirrection

and

$$(Vinitial)*cos(theta)$$
for the x dirrection

 

[thepatientmental]

It seems like you are on the right track with using the angle and sine in your calculations. The equation for calculating the initial velocity of a projectile is v = u*sin(theta), where v is the final velocity, u is the initial velocity, and theta is the angle of launch. So for the first part of the question, you would use 35 degrees as the angle and 5.80 m as the final displacement to solve for the initial velocity.

As for the second part of the question, you can use the same equation but with a 5% increase in the initial velocity. So the new equation would be v = (u + 0.05u)*sin(theta). You can then solve for the new displacement and compare it to the original 5.80 m to find the difference in length.

It's possible that your calculation of 3.32 is incorrect due to a mistake in the units or not using the correct angle in the equation. Double check your calculations and make sure you are using the correct values in the formula. If you are still having trouble, it may be helpful to consult with a teacher or tutor for further assistance. Good luck!