Awoman stands at a horizontal distance x from a mountain and measures the angle of elevation of the mountaintop above the horizontal as θ. after walking a distance d closer to the mountain on level ground, she finds the angle to be ϕ. find a general equation for the height y of the mountain in terms of d, ϕ, and θ, neglecting the height of her eyes above the ground.

Madison pushes with a 210-n horizontal force on a 24-kg crate of coffee resting on a warehouse floor. the force of friction on the crate is 74 n. what is the acceleration?

Asteel tube (k=50 w/mk) of inner and outer diameter di = 20mm and do=26mm, respectively, is used to transfer heat from hot gases flowing over the tube (h-hot = 200w/m2k) to cold water flowing through the tube (h-cold = 8000 w/m2k). what is the cold-side overall heat transfer coefficient uc? to enhance heat transfer 16 straight fins of rectangular profile are installed longitudinally along the outer surface of the tube. the fins are equally spaced around the circumference of the tube, each having a thickness of 2mm and a length of 15mm. what is the corresponding overall heat transfer coefficient uc? *solve for uc in both cases*

Vi. on another planet, a spring with constant 4.7 n/m is set up and allowed to expand verticaly freely. 8.4kg mass is placed on the spring and the spring extends 5.28m. calculate the exected extension on earth.