I figured out the 1st question but I do not understand the second one...please show me step by step! Thank you!

Nice work so far. I think if there's a problem with the second part, it's probably because you swapped the 'x' and 'y' components of the velocity in the first part.
If you just draw the line to complete the triangle in the first picture, it'll help you see that the vertical (y) component of the velocity is the side opposite the 35.2, so it's the sine of the angle. So Vy = -7.5 sin(35.2) = -4.32 m/s.
Similarly, the horizontal (x) component of velocity is adjacent to the angle, so it's the cosine. Vx = 7.5 cos(35.2) = 6.13 m/s.
You're doing fine work with the sin and cos, you just swapped the two. It's no major big deal.
So now let's look at the second part:
The 'x'-component of velocity doesn't change. because gravity can't do anything horizontally. So it's still 6.13 m/s .
They say that the object is now moving 58° below horizontal. Fine. Look at the cosine of that 58° ... it's 0.53 = (6.13 m/s) / (magnitude of velocity) .
Magnitude of velocity = 6.13 / 0.53 = 11.57 m/s .
(Where did all that extra velocity come from ? The y-component is growing steadily on account of the acceleration of gravity.)
I just looked at your work on the first part again. You even have the sin and cos in the right place ! But there was no need to go over to the other acute angle. Just stay with the 35.2 angle and everything will be beautiful. If for some reason you feel you absolutely must work with the 54.8°, then the 'x' is opposite it ==> sine, and the 'y' is adjacent to it ==> cosine. But you're really working with this stuff. I can tell you know what you're doing.

Answered by AL2006 | 2024-06-10

To solve the second part of the motion problem, we first separate the motion into horizontal (Vx) and vertical (Vy) components. With the initial horizontal velocity remaining constant and applying the angle given in the second part (58°), we calculate the total velocity to be approximately 11.57 m/s. This approach uses the trigonometric relationships governing motion in two dimensions, ensuring accurate results.
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Answered by AL2006 | 2024-12-24