Amountaintop is a height y above the level ground. a woman measures the angle of elevation of the mountaintop to be θ when she is a horizontal distance x from the mountaintop. after walking a distance d closer to the mountain, she measures the angle of elevation of the mountaintop to be φ. neglecting the height of the woman’s eyes above the ground, draw a well-labeled diagram representing this situation and find an expression for the height of the mountain, y, in terms of d, φ, and θ. note that your expression cannot contain x.

Ogle–2013–blg–0723 is an exoplanet that is similar to earth in size and proximity to its star. this exoplanet has mass m=4.18×1024kg and radius r=5.66×106m. an astronaut whose weight on earth is w=735n lands on the planet. a. calculate m, the mass of the astronaut. b. calculate gp? , the acceleration due to gravity on the surface of ogle–2013–blg–0723. c. calculate wp? , the weight of the astronaut on the surface of ogle–2013–blg–0723. d. calculate v, the minimum velocity required to put an object into orbit above ogle–2013–blg–0723. e. calculate t, the time required to complete an orbit around ogle–2013–blg–0723.

Find v(t), given acceleration a(t)=7j and initial velocity v(0)=k

The period of a pendulum varies directly as the square root of the length of the pendulum and inversely as the square root of the acceleration due to gravity. find the period when the length is 144 cm and the acceleration due to gravity is 980 cm per second squared, if the period is 7pi seconds when the length is 289 cm and the acceleration due to gravity is 980 cm per second squared.