Horizontal and vertical velocity components

[IAmSparticus]

Homework Statement

A dolphin leaps out of the water at an angle of 32° above the horizontal. The horizontal component of the dolphin's velocity is 7.7 m/s. Find the magnitude of the vertical component of the velocity.

Homework Equations

Vy=V0y + ayt

The Attempt at a Solution

4.63 m/s is incorrect.

cos(32 degrees) = (7.7 m/s) / hypotenuse

 

[tiny-tim]

Hi IAmSparticus!

Show us your full calculations, and then we can see what went wrong, and we'll know how to help!

 

[tomcue]

hypotenuse = 7.7 m/s / cos(32 degrees) = 9.06 m/s

The correct magnitude of the vertical component of the velocity is 9.06 m/s. This can be found using the trigonometric relationship between the horizontal and vertical components of a vector. The horizontal component is given as 7.7 m/s, and the angle of 32° allows us to use the cosine function to find the hypotenuse of the right triangle formed by the velocity vector. Therefore, the magnitude of the vertical component can be found by dividing the horizontal component by the cosine of the angle. This gives a magnitude of 9.06 m/s for the vertical component of the dolphin's velocity. It is important to note that this only gives the magnitude of the vertical component, and the direction of the velocity would also need to be considered for a more complete understanding of the dolphin's motion.