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Initial Speed given Maximum Height Formula

GoInitial Speed using Time of Flight Formula

GoInitial Velocity using Range Formula

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Initial Velocity is the velocity of an object at the start of a motion, describing the object's initial state of motion. Check FAQs

u = \frac{\sqrt{H max \cdot 2 \cdot g}}{\sin (θ pr)}

u - Initial Velocity?H_max - Maximum Height?g - Acceleration due to Gravity?θ_pr - Angle of Projection?

Initial Speed given Maximum Height Example

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Here is how the Initial Speed given Maximum Height equation looks like with Values.

Here is how the Initial Speed given Maximum Height equation looks like with Units.

Here is how the Initial Speed given Maximum Height equation looks like.

35.0038 = \frac{\sqrt{9.48 \cdot 2 \cdot 9.8}}{\sin (0.4)}

35.0038m/s = \frac{\sqrt{9.48m \cdot 2 \cdot 9.8m/s²}}{\sin (0.4rad)}

35.0038 = \frac{\sqrt{9.48 \cdot 2 \cdot 9.8}}{\sin (0.4)}

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Initial Speed given Maximum Height Solution

Follow our step by step solution on how to calculate Initial Speed given Maximum Height?

FIRST Step Consider the formula

u = \frac{\sqrt{H max \cdot 2 \cdot g}}{\sin (θ pr)}

Next Step Substitute values of Variables

∴

u = \frac{\sqrt{9.48m \cdot 2 \cdot 9.8m/s²}}{\sin (0.4rad)}

Next Step Prepare to Evaluate

∴

u = \frac{\sqrt{9.48 \cdot 2 \cdot 9.8}}{\sin (0.4)}

Next Step Evaluate

∴

u = 35.0038489126706m/s

LAST Step Rounding Answer

∴

u = 35.0038m/s

Initial Speed given Maximum Height Formula Elements

Variables

Functions

Initial Velocity

Initial Velocity is the velocity of an object at the start of a motion, describing the object's initial state of motion.

Symbol: u

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Initial Velocity

Maximum Height

Maximum Height is the highest point reached by an object under the influence of gravity or other external forces during its motion.

Symbol: H_max

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Maximum Height

Acceleration due to Gravity

Acceleration due to Gravity is the rate of change of velocity of an object under the influence of gravitational force, typically measured in meters per second squared.

Symbol: g

Measurement: AccelerationUnit: m/s²

Note: Value should be greater than 0.

Formulas to find Acceleration due to Gravity

Angle of Projection

Angle of Projection is the angle at which an object is projected from the ground, influencing its trajectory and range of motion.

Symbol: θ_pr

Measurement: AngleUnit: rad

Note: Value can be positive or negative.

Formulas to find Angle of Projection

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Initial Velocity

Go Initial Speed using Time of Flight

u = \frac{T \cdot g}{2 \cdot \sin (θ pr)}

Go Initial Velocity using Range

u = \sqrt{g \cdot \frac{R motion}{\sin (2 \cdot θ pr)}}

Other formulas in Projectile Motion category

Go Maximum Height Attained for Inclined Projectile

H max = \frac{{(u \cdot \sin (θ inclination))}^{2}}{2 \cdot g \cdot \cos (α pl)}

Go Time of Flight for Inclined Projectile

T = \frac{2 \cdot u \cdot \sin (θ inclination)}{g \cdot \cos (α pl)}

Go Maximum Range of Flight for Inclined Projectile

R motion = \frac{u^{2} \cdot (1 - \sin (α pl))}{g \cdot {(\cos (α pl))}^{2}}

Go Maximum Height Attained by Object

v max = \frac{{(u \cdot \sin (θ pr))}^{2}}{2 \cdot g}

How to Evaluate Initial Speed given Maximum Height?

Initial Speed given Maximum Height evaluator uses Initial Velocity = (sqrt(Maximum Height*2*Acceleration due to Gravity))/sin(Angle of Projection) to evaluate the Initial Velocity, Initial Speed given Maximum Height formula is defined as a measure of the initial velocity of an object under the sole influence of gravity, considering the maximum height it can reach, and the angle of projection, providing valuable insights into the kinematics of motion. Initial Velocity is denoted by u symbol.

How to evaluate Initial Speed given Maximum Height using this online evaluator? To use this online evaluator for Initial Speed given Maximum Height, enter Maximum Height (H_max), Acceleration due to Gravity (g) & Angle of Projection (θ_pr) and hit the calculate button.

FAQs on Initial Speed given Maximum Height

What is the formula to find Initial Speed given Maximum Height?

The formula of Initial Speed given Maximum Height is expressed as Initial Velocity = (sqrt(Maximum Height*2*Acceleration due to Gravity))/sin(Angle of Projection). Here is an example- 78.76481 = (sqrt(9.48*2*9.8))/sin(0.4).

How to calculate Initial Speed given Maximum Height?

With Maximum Height (H_max), Acceleration due to Gravity (g) & Angle of Projection (θ_pr) we can find Initial Speed given Maximum Height using the formula - Initial Velocity = (sqrt(Maximum Height*2*Acceleration due to Gravity))/sin(Angle of Projection). This formula also uses Sine (sin), Square Root (sqrt) function(s).

What are the other ways to Calculate Initial Velocity?

Here are the different ways to Calculate Initial Velocity-

Initial Velocity=(Time of Flight*Acceleration due to Gravity)/(2*sin(Angle of Projection))
Initial Velocity=sqrt(Acceleration due to Gravity*Range of Motion/sin(2*Angle of Projection))

Can the Initial Speed given Maximum Height be negative?

No, the Initial Speed given Maximum Height, measured in Speed cannot be negative.

Which unit is used to measure Initial Speed given Maximum Height?

Initial Speed given Maximum Height is usually measured using the Meter per Second[m/s] for Speed. Meter per Minute[m/s], Meter per Hour[m/s], Kilometer per Hour[m/s] are the few other units in which Initial Speed given Maximum Height can be measured.

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