Projectile Motion given 2 position equation

[steph35]

Homework Statement

The motion of a human body through space can be precisely modeled as the motion of a particle at the body's center of mass. The components of the displacement of an athlete's center of mass from the beginning to the end of a certain jump are described by the two equations below, where t is the time at which the athlete lands after taking off at time t = 0.

xf =0 + (11.1 m/s)(cos 20.3°)t
0.369 m = 0.812 m + (11.1 m/s)(sin 20.3°)t - 1/2(9.80 m/s2)t2

Homework Equations

(a) Identify his position.
? meters ihat + ? meters jhat
(b) Identify his vector velocity at the takeoff point.
? m/s at ? ° above horizontal
(c) The world long jump record is 8.95 m. How far did the athlete in this problem jump?
? m

The Attempt at a Solution

So, I drew out a diagram and it seemed to make sense to me but the answers were wrong. for a) i got you would just take the component vectors, so Vxi= (11.1 m/s)(cos 20.3) and Vyi= (11.1 m/s) (sin20.3). But that was wrong. I got b). and for c) i thot you could jus pick out the information and it would be .369 but then realized that is only in the y direction, but time isn't give, so how are we supposed to find the x_final?

 

[LowlyPion]

Homework Statement

The motion of a human body through space can be precisely modeled as the motion of a particle at the body's center of mass. The components of the displacement of an athlete's center of mass from the beginning to the end of a certain jump are described by the two equations below, where t is the time at which the athlete lands after taking off at time t = 0.

xf =0 + (11.1 m/s)(cos 20.3°)t
0.369 m = 0.812 m + (11.1 m/s)(sin 20.3°)t - 1/2(9.80 m/s2)t2

Homework Equations

(a) Identify his position.
? meters ihat + ? meters jhat
(b) Identify his vector velocity at the takeoff point.
? m/s at ? ° above horizontal
(c) The world long jump record is 8.95 m. How far did the athlete in this problem jump?
? m

The Attempt at a Solution

So, I drew out a diagram and it seemed to make sense to me but the answers were wrong. for a) i got you would just take the component vectors, so Vxi= (11.1 m/s)(cos 20.3) and Vyi= (11.1 m/s) (sin20.3). But that was wrong. I got b). and for c) i thot you could jus pick out the information and it would be .369 but then realized that is only in the y direction, but time isn't give, so how are we supposed to find the x_final?

For a) you identified his components of velocity as his position.
But the question asked about the Position P_(t) in terms of the unit vectors.

For c) you have two equations in t. Once you solve for t, you can determine x.

 

[steph35]

all right, i got the t and solved c.

however, for a) I am still a bit confused. are they asking for his initial position? becuase if they are wouldn't it be 0 for ihat and .443 jhat? i got the 0 ihat correct, but the.443 was wrong?

 

[LowlyPion]

all right, i got the t and solved c.

however, for a) I am still a bit confused. are they asking for his initial position? becuase if they are wouldn't it be 0 for ihat and .443 jhat? i got the 0 ihat correct, but the.443 was wrong?

I'm going to say that I think it is worded poorly. If it is initial position that is asked for, then it will be the x=0 and y=.812 at t=0 The final position is a consequence of his jump and as far as initial position is concerned is not a factor.

My initial reading of the question suggested to me they wanted the unit vectors as a function of the time. But if x=0 is the coefficient of i-hat then I suppose initial condition is what they asked. But I am not entirely happy with that interpretation.