Kids are playing ball for recess. The ball is kicked from the ground with an initial velocity of 50ft/sec. Use the projectile motion equation to determine how long the catcher has to get into position it be catches the ball 6 feet in the air on its way down.

0.12  s

Step-by-step explanation:

initial velocity of projection, u = 50 ft/s

range, R = 6 feet

Let θ is the angle of projection.

Use the formula for the horizontal range.

Sin 2θ = 0.0768

2θ = 4.4 degree

θ = 2.2 degree

The formula for the time of flight is

T = 2 u Sin θ/g

T = 2 x 50 x Sin 2.2 / 32

T = 0.12 second

thus, the time required is 0.12 s.

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.

correct choice is b

step-by-step explanation:

when you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. for the function the average rate of change from point to point can be calculated as

to find the average rate of change from day 2 to day 10, note that at day 2, 8 houses were sold, so a(2,8) and at day 10, 2 houses were sold, so b(10,2). thus,