You and your friends find a rope that hangs down 15 m from a high tree branch right at the edge of a river. You find that you can run, grab the rope, swing out over the river, and drop into the water. You run at 2.0 m/s and grab the rope, launching yourself out over the river.

Vertical angle=9.5°

Time to reach maximum height = 1.24seconds

Step-by-step explanation:

The maximum distance x is reached when rope swings to a maximum height, maximum height is gotten from the equation KE= 1/2MU^2 = MgH = MgL= Mgl(1- cos theta.

Where theta is the vertical angle, U=2m/s and L= 15m

2gl -2glcostheta=U^2

2gl U^2=2gl cos theta

But theta= Acos(1- U^2)/2gl

Acos(1-/(2×9.8×15)

Theta =9.5°

Maximum height li given by

Lsintheta

But X= UxT

T=X/UX= Lsintheta/U = 15sin9.5 /2 =1.24seconds

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.

d. it is a convex pentagon because it has five sides and none of the sides would extend into the inside of the polygon.

step-by-step explanation: