Question bank: Quadratic Equation: Bhaskara

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Question 1:

Medium

A farmer wants to plant a new crop and needs to fence a rectangular area with one side along a river, without needing a fence along the river. He has 1000 meters of fence and intends to maximize the fenced area. Suppose the length of the fence parallel to the river is x meters and the width of the fenced area is y meters. The area A can be given by A = x * y. Determine the dimensions of the fenced area to obtain the maximum area?

Quadratic Equation: Bhaskara

Question 2:

Medium

Quadratic Equation: Bhaskara

Theorical Question

Question 3:

Easy

Quadratic Equation: Bhaskara

Question 4:

Hard

A projectile is launched from the ground with an initial velocity of 40 m/s, forming an angle of 60 degrees with the horizontal. Disregarding air resistance and considering gravity acceleration as 10 m/s², the maximum range of the projectile can be determined by solving a second-degree equation that models the projectile's parabolic trajectory. Use the Bhaskara formula to find the roots of this equation, where 'x' represents the horizontal distance traveled by the projectile and the coefficients 'a', 'b', and 'c' are obtained from the components of the initial velocity and gravity acceleration. Based on this data, determine the maximum range of the projectile.

Quadratic Equation: Bhaskara

Contextualized Question

Calculus Question

Question 5:

Medium

Imagine you are an engineer and need to calculate the maximum height a projectile reaches when launched from the ground with an initial velocity of 40 meters per second and an angle of 60 degrees relative to the ground. The height reached by the projectile can be represented by a quadratic function where t is the time elapsed in seconds, v0 is the initial velocity in meters per second, and α is the angle measured in degrees. Write the equation h(t) using the provided data. Find the maximum height using the vertex form of a parabola and indicate the time at which the projectile reaches this height.

Quadratic Equation: Bhaskara

IARA TIP

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