Aprojectile is launched vertically from the ground into the air with initial velocity v0. it reaches the ground in 10 minutes. assume that the height of the projectile above the ground after t minutes is given by h(t) = −5t 2 + v0t. find the initial velocity v0 of the projectile.

The initial velocity of the projectile is 50 meters per minute

Explanation:

The equation that describes the height (h on meters) of the projectile as a function of time (t in minutes) is:

(1)

We already know at 10 minutes the projectile reaches the ground, so if we assume our coordinate system on the ground that implies h(10 min)=0m, using this on (1):

solving for :

Note: It’s important to have a careful use of units in this kind of problem to avoid errors in the units of our answers, if we are calculating velocity we should get velocity units.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west

this is an example of "committed" time.

committed time, as contracted time, takes need over essential and available time since it is seen as profitable work. it alludes to the time allotted to keep up a home and family. at the point when a man is commuting using committed time this individual may feel that the drive is an obligation to family, for example, strolling youngsters to class or driving a mate to work. contracted and committed time clients may feel that their commute could really compare to the commute of important or leisure time clients on the grounds that their commute is profitable work. in this manner, they might be more disposed to pick a mechanized method of movement.