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A basketball tosses a ball to a teammate. The ball reaches a maximum height of 11 feet 3 seconds after it was released. If the b

labwork [276]

Answer:

h = - 16t² + 49.67t + 6

Step-by-step explanation:

The expression for the height of the basketball, h at time, t is given by

h - h₀ = u₀t - 1/2gt² where h₀ = initial height of ball = 6 feet, h = maximum height of ball = 11 feet, u₀ = initial vertical velocity of ball, t = time taken to reach maximum height = 3 s and g = acceleration due to gravity =9.8 m/s².

We need to find u₀ from u = u₀ -

So, h - h₀ = u₀t - 1/2gt²

h - h₀ + 1/2gt² = u₀t

u₀ = (h - h₀)/t + 1/2gt

substituting the values of the variables into the equation, we have

u₀ = (h - h₀)/t + 1/2gt

u₀ = (11 ft - 6 ft)/3s + 1/2 × 32 ft/s² × 3 s

u₀ = 5 ft/3s + 1/2 × 96 ft/s

u₀ = 1.67 ft/s + 48 ft/s

u₀ = 49.67 ft/s

Using h - h₀ = u₀t - 1/2gt² where h is the height of the basketball at time, t

h = u₀t - 1/2gt² + h₀

substituting the values of the variables into the equation, we have

h = u₀t - 1/2gt² + h₀

h = (49.67ft/s)t - 1/2(32 ft/s²)t² + 6 ft

h = 49.67t - 16t² + 6

h = - 16t² + 49.67t + 6

3 0

3 years ago

Mark and Robyn used base- ten blocks to show that 200 is 100 times as much as 2. Whose model makes sense? Whose model is nonsens

Dima020 [189]

Answer:

Robyn model makes more sense and Marks is nonsense.

Step-by-step explanation:

In this question ,calculations not required .All we have to do is consider each model logically .

Marks

Marks model shows 20 rather than 2 which means 200 is 10 times as much as 20. It does not make any sense.

Robyn

Robyn model shows 2 which means 200 is 100 times as much as 2 and this is not only correct but also makes sense because 100 *2=200

8 0

3 years ago

Given: KLMN is a trapezoid, KF =10 MF ║ LK AKLMF = AFMN Find: KN

Nimfa-mama [501]

You can see the trapezoid in the attached picture.

The data given in the problem are:
KF = 10
LK // MF
A(KLMF) = A(FMN)

We know that KLMF is a parallelogram because:
LM // KF (bases of the trapezoid)
LK // MF (hypothesis).
The area of a parallelogram is given by the formula:
A(KLMF) = b × h
 = KF × h
 = 10 × h

The area of a triangle is given by the formula:
A(FMN) = (b × h) / 2
 = (FN × h) / 2

The problem states that the two areas are congruent, therefore:
A(KLMF) = A(FMN)
10 × h = FN × h / 2
10 = FN / 2
FN = 20

Therefore we can calculate:
KN = KF + FN = 10 + 20 = 30

Hence, KN is 30 units long.